Chapter - 1

CHAPTER REFLECTION OF LIGHT 1 AT CURVED SURFACES TOPICS / SYLLABUS Reflection of Light at Curved Surfaces : Weightage Marks 1 VSAQ 02 Marks 1. Reflection of light by spherical mirrors 0 SAQ 00 Marks 2. Ray diagrams for Concave mirror & Convex 0 LAQ 00 Marks 1 MCQ 01 Mark mirrors Total Marks 03 Marks 3. Derivation of formula for curved mirrors 4. Sign convention for the parameters related to the mirror equation 5. Magnification (m) 6. Making of Solar Cooker 7. Applications of Concave & Convex mirrors Author’s Note : This chapter is important for VSAQs and MCQs. Generally, one VSAQ and one MCQ are asked from this chapter every year. This chapter is worth 2 + 1 = 3 Marks. Ray diagrams for convex and concave mirrors, problems based on mirror formula, magnification of images, usews of concave and convex mirrors, formation of images at different places, sign conventions, are the most important topics from the examination point of view in this chapter. Chapter at a Glance 1. Reflection of Light by Spherical Mirrors: ¾¾ Reflection of light : • The phenomenon of sending back of light rays Normal in the same medium when they are incident on a smooth polished surface like mirror is called Incident ray Reflected ray reflection of light. In short, “The bouncing ir Angle of reflection back of rays of light from a polished and shiny Angle of incidence surface is called reflection of light.“ O • Reflection of light occurs when the waves Point of incidence encounter a surface or other boundary that does not absorb the light energy of the Reflection of light from a plane polished surface radiation and bounces the waves away from the surface. • Silver and Mercury are the best metals used as reflectors of light in all types of mirrors. ¾¾ Fermat Principle : ¾¾ According to Fermat, “Light chooses the path which takes the least time to travel”. It is also applicable to reflection of light.  Laws of Reflection of Light : When light undergoes reflection from a smooth polished surface, it obeys two laws which are known as the “Laws of reflection of light”.

2 (T.S.) PHYSICAL SCIENCE – Class 10  First law : The first law states that, “The incident ray, the reflected ray and the normal at the points of incidence all lie in the same plane.”  Second law : The second law states that, “The angle of incidence is equal to the angle of reflection i.e., ∠i = ∠r.” These laws of reflection are applicable to all types of reflecting surfaces including spherical surfaces. ¾¾ Mirrors : Mirrors are the basic means of viewing our own beauty. Definition :A smooth highly polished surface is called a mirror. Generally mirrors refer to plane mirrors. But if the surface of a mirror is curved it is said to be a curved mirror. If the curved mirror is a part of a huge sphere, then the mirror is a spherical mirror. Depending upon the reflecting surface, mirrors are classified into two types. They are : 1) Plane mirror and 2) Curved mirror. 1) Plane mirror : A highly polished plane surface is called a plane mirror. 2) Spherical Mirror : A mirror in which the reflecting surface is curved is called a spherical mirror. Depending upon the type of curve, spherical mirrors are of two types: 1) Concave mirror : A spherical mirror whose outer side is silvered(polished) and inner side the reflecting surface is called a concave mirror. A concave mirror works like a convex lens. 2) Convex mirror : A spherical mirror whose inner side is silvered(polished) and outer side the reflecting surface is called a convex mirror. Reflecting surface Reflecting Polished Reflecting Polished surface surface surface surface Polished surface Plane Mirror Concave Mirror Convex Mirror Terms Related to Reflection of Light : 1) Incident ray : The ray of light that falls on the reflecting surface is called the incident ray. 2) Reflected Ray : The ray of light that gets reflected back in the same medium from the reflecting surface is called a “Reflected Ray.” 3) Normal : A line segment perpendicular to the plane of the reflecting or refracting surface at the point of incidence is called Normal. 4) Angle of Incidence : The Angle of Incidence is the angle formed by the incident ray and the normal at the point of incidence. 5) Angle of Reflection : The angle between the reflected ray and the normal at the point of reflection is called the “Angle of Reflection.” Terms Related to Spherical Mirrors : 1) Aperture :The aperture is the effective width of the mirror from which reflection can occur. 2) Pole : The pole of a spherical mirror is its center. It is denoted by the letter P. 3) Centre of Curvature : The geometrical centre of the hollow sphere of which the spherical mirror is a part is called the Centre of Curvature (C). 4) Radius of Curvature : The radius of the hollow sphere of which the spherical mirror is a part is called the Radius of Curvature (r). Greater the radius of curvature of the sphere, greater is the focal length (R = 2f).

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 3 5) Principal axis : The straight line passing through the centre of curvature C and the pole P of the spherical mirror is called principal axis. 6) Principal focus (Focus) : The principal focus (F) of a spherical mirror is the point on the principal axis where all rays of light incident on the mirror, parallel to the principal axis, meet or appear to come from after reflection. 7) Focal length : The distance between the pole and principal focus of the mirror is called the focal length of the mirror. It is represented by the symbol ‘ f ‘ and is always half the radius R of curvature i.e., f = 2 . Shorter focal length implies larger converging/diverging power. Images : The point  of convergence or the point from where the light appear to diverge after reflection or refraction is called an Image. Images are of the two types. They are : (1) Real image, and (2) Virtual image. 1) Real image : If two or more light rays after reflection or refraction actually meet at a point the image formed is known as the real image. Characteristics of Real Image : • A real image can be obtained on the screen. • It is always inverted (up side down with respect to the objects). • The size of the real image depends on the position of the object so it can be diminished, or of the same size as that of the object or enlarged. • It is formed by both concave mirror and convex lens. Mirror 2) Virtual image : If the rays do not actually meet but appear to meet at a point when extended backwards, the image is called a virtual image. Characteristics of Virtual Image : • A virtual image cannot be obtained on the screen. • It is always erect i.e., upside up with respect to the object. • The size of the virtual image depends on the nature of mirror. • It is formed by concave, convex and and plane mirrors. 2. Ray Diagram for Concave & Convex mirror : To draw ray diagrams, we have to follow the rules of reflection for concave mirrors: Ray diagrams: While drawing ray diagrams, the important rules regarding the placement of the object are as follows : 1) The reflecting surface must face towards the left side. 2) The object(O) must be kept perpendicular to the principal axis such that its foot touches it. Construction of Images using Ray Diagrams : You know that an infinite number of rays travel from any point on an object. In order to obtain the image of an object we need to know at least two incident rays whose paths after

4 (T.S.) PHYSICAL SCIENCE – Class 10 reflection from the mirror are known. Any two of the following rays can be taken as the convenient incident rays for locating the image. 1) An incident ray passing through the Centre of Curvature (C) : An incident ray passing CF P In case of a convex P FC through the centre of mirror, an incident ray b. Convex mirror curvature of a concave a. Concave mirror which appears to move mirror reflects back towards the direction along the same path, of centre of curvature without any deviation. is reflected back in the same path without any deviation. 2) An incident ray parallel to the principal axis : In case of a concave CF P In case of a convex P FC mirror, an incident mirror, the incident b. Convex mirror ray parallel to the a. Concave mirror ray passing parallel principal axis passes to principal axis, after through the focus reflection appears to after reflection. come from the focus of the mirror. 3) An incident ray passing through the focus : In a concave mirror, CF P In case of a convex FC an incident ray mirror, the incident ray b. Convex mirror passing through a. Concave mirror after reflection appears the focus is to come from the focus P reflected parallel to of the mirror and is the principal axis. reflected parallel to the principal axis. 4) A ray of light incident at the pole of the mirror : In a concave mirror, a ray of CF i This is also i light incident at the pole gets rP true for C FrP reflected along a path such a convex that the angle of incidence is a. Concave mirror mirror b. Convex mirror equal to the angle of reflection ∠i = ∠r. ∠i = ∠r. Images formed by Concave mirror : Different positions of the Object and Images formed by Concave mirror : Position of Position of Nature and Ray Diagram Sign Object Convention Image size of Image At infinity (∞) At Focus(F) Real, inverted B u, v and f are & highly F P all –ve diminished A

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 5 A' u, v and f are all –ve Beyond C Between f Real, inverted B &C & diminished u, v and f are B' C F P all –ve A u, v and f are all –ve BD At C At C Real, inverted A F P & same size A' C E B' Between f & C Beyond C Real, inverted A F D & enlarged B' P CB E A' Real, inverted B u, v and f are At F At infinity & highly A all –ve F enlarged u and f B are –ve Between F and Behind the Virtual, C FA P v is +ve P mirror enlarged and C erect image B' D P A' Images formed by Convex mirror : Different Positions of the Object and Images Formed by Convex mirror : Position of the Position of the Nature of the object images images A M At infinity ∞ At focus (F) Virtual, erect and PF C behind the mirror highly diminished N B At infinity Between ∞ and Between P & F Virtual, erect and A X C pole of the mirror behind the mirror diminished D B Object E A' P B' F Image M

6 (T.S.) PHYSICAL SCIENCE – Class 10 Remember : 1. Real images are those where light actually converges. 2. Virtual images are locations from where light appears to have converged. 3. Real images are formed when the objects are placed outside the focal length of a converging mirror. 4. Virtual images are formed by placing an object inside the focal length of a converging lens. 5. The image distance is positive for real image and negative for virtual images. 6. Height of the image and object are positive if measured upwards from the axis and negative if measured down under the axis. Relation between radius of curvature and focal length : The focal length of a spherical mirror is equal to half of its radius of curvature (both convex as well as concave mirror). (O R ) The radius of curvature is twice the focal length (R) = 2f Mathematically, Focal length = Radius of curvature 2 R or f = 2 or R = 2f 3. Derivation of Formula for Curved Mirrors : • Formula gives the relationship between image distance (v) , object distance (u) and the focal length ( f ) of the mirror. It is written as : Mirror Formula : 1 = 1 + 1 f v u • Where f = focal length, v = the image distance, and u = the object distance. • This formula is valid for concave and convex mirrors in all situations for various positions of the object. Important points in using the mirror formula : 1) Put the correct signs of known variables according to the sign convention. 2) Do not put the sign of an unknown variable. The sign will automatically come up during calculations. 3) If the calculated sign turns out to be positive, then the variable calculated is behind the mirror. However, if calculated sign turns out to be negative, then variable is to be infront of the mirror. 4. New Cartesian sign conventions for the parameters related to the mirror equation : Definition : The set of rules, to use ‘+’ or ‘–’ sign with the values while solving any problems in optics is called sign convention. They are : • The object is always placed to the left of the mirror, so that incident light moves left to right.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 7 • All distances are to be measured from the pole of the mirror i.e., from origin of coordinate axis. • The distances measured in the direction of the incident light will be taken as +ve, and those measured in the direction opposite to incident light will be taken as –ve. • All measured of height above the principal axis are to be taken as positive (+ve) and below are taken as negative (– ve). Diagrammatic Explanation of Cartesian sign conventions : Object on the left Direction of incident light MY A Distance along incident light (+ve) Height Pole P upwards Distance against incident light (–ve) N Y' Positive (+ve) B' X' BF X Height Mirror downwards A' Negative (–ve) 5. Magnification : • Magnification is the increase in image size produced by spherical mirrors with respect to the object size. The magnification may be linear or transverse. • In simple words, magnification or linear magnification may be defined as “the ratio of the size of the image (hi) to the size of the object (ho)”. It is denoted by m. • The magnification (m), produced by a spherical mirror can be expressed as : m = Height of the image (hi) =  hi  = − v  on applying sign convention. Height of the object (ho)  ho  u    • Magnification is also equal to the ratio of image distance to the object distance. − v  u  Important points in using magnification formula: • Magnification (m) is negative (–ve) for real and inverted images whereas it is positive (+ve) for virtual images. So magnification is always –ve for a convex mirror, while it depends on position of object in concave mirror. • If, i) m < 1, image is diminished ii) m > 1, image is enlarged iii) m = 1, image is of the same size of the object. 6. Making of Solar Cooker : • Make an wooden/iron frame in the shape of TV dish. • Cut acrylic mirror sheets into 8 - 12 pieces in the shape FP of isosceles triangles with a height equal to the radius of your dish antenna. • The bases of 8 - 12 triangles together makes the circumference of the dish. • Stick the triangle mirrors to the dish as shown in figure. Ray Diagram for Solar Cooker Your solar heater cooker is ready. • Arrange it so that concave part faces sun. • Find its focal point and place a vessel at that point. The vessel gets heated enough to cook rice.

8 (T.S.) PHYSICAL SCIENCE – Class 10 7. Application of concave and convex mirror : Uses of concave mirror : 1) It is used as shaving mirror. 2) It is used as a reflector to concentrate light in solar cookers. 3) It is also used in reflecting type astronomical telescope. 4) It is also used in search light, head light of automobiles etc. 5) It is used by dentists to observe cavities in the teeth. 6) It is also used in ophthalmoscope, to examine eye, nose throat and ear of a person. Reasons for various uses of Concave mirror 1. Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. 2. They are often used as shaving mirrors to see a larger image of the face. The dentists use concave mirrors to see large images of the teeth of patients. 3. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces. Uses of convex mirror : It is used : 1) as a rear view mirrors in automobiles. 2) as a device to check theft in shops. 3) to bring view of corners which are not directly accessible. 4) to light a large area. Reasons for various uses of Convex mirror 1. Convex mirrors are preferred because they : a) gives a wider field of view as the mirror is curved outward. b) produces erect and diminished image of the traffic behind the driver of the vehicle. 2. Thus, convex mirrors enable the driver to view much larger area than would be pos- sible with a plane mirror. KEY WORDS : Meanings  and  Explanations 1. Centre of : Centre of curvature is a centre of hollow sphere of which the mirror is Curvature a part. 2. Radius of : The radius (distance between vertex and centre of curvature) of the Curvature hollow sphere of which the spherical mirror is a part is called Radius of Curvature. 3. Principle axis : The horizontal line which passes through the centre of curvature and 4. Focus / Focal pole is called Principle axis. point : The principal focus (F) of a spherical mirror is the point on the principal axis where all rays of light incident on the mirror, parallel to the Principal axis, meet or appear to come from after reflection.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 9 5. Focal length : The distance between the pole and the principle focus is called the focal 6. Object distance length of the spherical mirror. It is denoted by ' f '. 7. Image distance 8. Virtual image : The distance between object & mirror is called object distance. 9. Real image 10. Magnification : The distance between image & mirror is called image distance. 11. Ray diagrams : The image formed by controlled rays of reflection is called virtual image. 12. Aperture This cannot be caught on the screen. : The image formed by actual intersection of reflected rays is called real image. This can be caught on the screen. : Magnification is defined as the ratio of the size of the image (hi) to the size of the object (ho) i.e., hi (Or) ho . It is the ratio of the height of the image to the height of the object and represented by the letter ‘m’ : A diagram showing the path of selected rays through an optical system. : The area of the mirror from which reflection takes place is called its Aperture. FLOW CHART REFLECTION MIRRORS Plane Mirror Spherical Mirror Characteristic of Concave Mirror Convex Mirror Image formed between vertex and focus Plane mirror Always Diverges Generally converges Diverges Real, inverted either Always virtual Erect, virtual diminished or enlarged diminished image enlarged

10 (T.S.) PHYSICAL SCIENCE – Class 10 INTEXT - QUESTIONS - ACTIVITY - LAB ACTIVITY Q. Is the image formed by a bulged surface same as the image formed by a plane mirror?  A. No, the image formed by a bulged surface is not same as the image formed by a plane mirror due to refractive index. It is a little bit bigger than the image formed by plane mirror. Q. Is the mirror used in automobiles a plane mirror ? Why does it show small images ?   A. 1) No, it is not a plane mirror . It is a convex mirror. 2) It shows small images because of the convergence of light rays. Q. Why does our image appear thin or bulged out in some mirrors?    A. 1) The type of image formed in a mirror depends on the reflecting surface. If the mirror has a plane reflecting surface the image formed will be the same size as the object. 2) If we stand in front of the mirror that is bulged outwards and mirror bent at the top and bottom, our image will be of small size and we look fatty. Whereas if we look in a mirror that is bulged in and bent at sides our image appears thin. 3) Thus, we can conclude that our image appear thin or bulged out in some mirrors because of : i) thickness of the mirror at various points. ii) bulging of mirrors outwards and inwards. iii) uneven surface of the reflecting surface at all points. Q. Can we see inverted images in any mirror?    A. 1) Yes in spherical mirror (Concave mirror) we can see inverted images. 2) In a plane mirror, if we place an object at the top we get an inverted image. Q. Can we focus sunlight at a point using a mirror instead of magnifying glass?    A. 1) Yes we can focus sun light at a point using a concave mirror. This happens because it is a converging mirror. (OR) 2) By using black paper with a -hole at its centre. Q. Are the angle of reflection and angle of incidence also equal for reflection by curved surfaces? A. 1) Yes the angle of reflection and angle of incidence are equal for all types of mirrors. This is because the laws of reflection are applicable to all types of reflecting surfaces. This has been stated in 2nd Law of reflection. 2) According to 2nd Law of reflection, “the angle of incidence is equal to the angle of reflection i.e., ∠i = ∠r.” ACTIVITY-1 : Finding the Normal to a Curved Surface :    Q. List out the materials required to find the normal to a curved surface. Write the procedure of the experiment with result. (OR) Explain with an activity the method to find the normal to a curved surface. (OR) By an activity, find the normal to the curved surface. A. AIM : To find the normal to a curved surface. MATERIALS REQUIRED : Thin foam or a rubber sole piece, 5-10 alpins. PROCEDURE : 1) Take a small piece of thin foam or rubber (just like the sole of a slipper) and fix small pins along a straight line on the foam as shown in fig 1(a). 2) See that all the pins fixed must be perpendicular to the foam. 3) If the foam is considered as a mirror, each pin would represent the normal at that point.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 11 4) Any ray incident at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin-normal. 5) Now bend the form piece inwards as depicted in the fig 1(b). It appears as a converging mirror. The pins represent the normal at various points. fig-1(a) fig-1(b) fig-1(c) fig - 1 (a) fig - 1 (b) fig - 1 (c) 6) Now if we bend the foam piece outwards, we will see that the pins seem to move away from each other and act like diverging mirror. Such mirrors are called convex mirrors. 7) This gives us a clue about how we can find normal to any point on a spherical mirror. 8) The only thing is we have to draw a line from the point on the mirror to the centre of the sphere. Result : The line drawn from C to any point on the mirror, gives the normal at that point. Activity Based Questions : Q. How does the incident ray reflect at the point where the pin makes contact with the surface? A. The incident ray at the point where the pin makes contact with the surface will reflect with the same angle as the incident ray made with the pin-normal. Q. If the piece of foam is bent inwards, how it acts? A. If the piece of foam is bent inwards, then it acts like convergent mirror (concave mirror). Q. If we bend a piece of foam outwards what do you observe? A. It is observed that : a) All the pins tend to converge at a point. b) The bent piece of foam acts like diverging mirror (convex mirror). Q. What do you conclude from the above activity ? A. Conclusion : 1) It gives an idea about the nature of spherical mirrors. 2) A rubber sole bent inwards will look like a concave mirror and outwards will appear like a convex mirror. 3) For a concave mirror all the normals (like the pins) will converge towards a point called as centre of curvature (C) of the mirror. 4) For the ray ‘R’ the incident angle is the angle it makes with the normal (i) and the reflected angle is as ‘r’. According to the first Law of Reflection ∠i = ∠ r. ACTIVITY-2 : Finding the Focus or Focal Point ( F ) and Focal Length ( f ) of the Spherical Mirror:   (Pg–4) Q. Write the materials required in the experiment to find focus or focal point ( F ) of the concave mirror. Describe its procedure. What do you understand by focus and focal length (OR) How do you find the focal point, focal length of the spherical mirror using an activity. A. AIM : To find the focal point and focal length of an spherical mirror (concave or convex). M AT E R I A L S R E Q U I R E D : A plain sheet (paper), convex or concave mirror, object (like sun or candle)

12 (T.S.) PHYSICAL SCIENCE – Class 10 PROCEDURE : 1) Hold a concave mirror perpendicular to the direction of sunlight. 2) Take a small paper and slowly move towards the mirror till the smallest and the brightest image is obtained on it and observe. OBSERVATION : 3) The rays coming from the sun parallel to the principle axis of concave mirror converge to a point. This point is called focus or focal point ( F ) of the concave mirror. 4) Measurethedistanceofthisspotfromthepoleofthemirror.Thisdistanceiscalledthefocallength ( f ) of the mirror. CONCLUSION / RESULT : 1) The point where the image of the sun is formed on the paper sheet is called focus or focal point ( F ) of the concave mirror. 2) The distance measured from the image to the pole of the mirror is called the focal length ( f ) of the mirror. Activity Based Questions : Q. What happens if you hold the paper at a distance shorter than the focal length from the mirror and move it away ?    A. The paper at first begins to burn producing smoke. Eventually it may even catch fire. This is because the light from the Sun is converged at a point, as a sharp, bright spot by the mirror. In fact, this spot of light is the image of the Sun on the sheet of paper. This point is the focus of the concave mirror. The heat produced due to the concentration of sunlight ignites the paper. The distance of this image from the position of the mirror gives the approximate value of focal length of the mirror. Q. Does the image of the sun become smaller or bigger ?    A. At first, the image of the sun is bigger. As we move the paper in front of the mirror, we find the image of the sun become smaller. It is sharp and at the point of focus. Think and Discuss Q. See figure below. A set of parallel rays are falling on a Convex mirror. What conclusion can you draw from this?    PF C A. When a set of parallel rays are incident on a convex mirror after reflection they appear to meet at the back of the mirror at a point called focus (F). Q. Will you get a point size image if you place a paper at the focal point ?    A. When the object is placed at the focal point, no image is formed. So, we can never get a point size image of the object placed at the focus of the convex mirror.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 13 LAB ACTIVITY Q. What are the materials required for the experiment to observe the various types of images formed by a concave mirror and measure the object distance and image distance from the mirror. Write the procedure of the experiment. Tabulate the result of the various types of images formed and their nature.    (OR) Explain with an experiment the various types of images formed by a concave mirror and measure the object and image distance from the mirror and note down them in tabular form. A. AIM : To observe the types of images formed and measure the object distance (u) and image distance (v) from the mirror. MATERIALS REQUIRED : A candle, paper, concave mirror, V-stand, measuring tape or meter scale. PROCEDURE : 1) Place the concave mirror on V-stand, a candle and meter scale shown in fig. 2) Keep the candle at different distances from the mirror (say 10 cm to 80 cm) along the axis by moving the paper (screen). 3) Find the position where you get the sharp image on paper by taking care that the flame is above the axis of the mirror and paper is below the axis. 4) Note down your observations in the given table : OBSERVATIONS : Table : 1 Observation Distance of candle from Distance of paper from Bigger / smaller Inverted No. mirror (object distance u) mirror (image distance v) than object or erected 1. 2. 3. 4. RESULT : Images formed by a concave mirror for different positions of the object are classified as follows : Table : 2 Position of the object Position of the image Nature of the image 1. At infinity At F Real, inverted and highly diminished 2. Between P and F Behind the mirror Virtual, erect and enlarged 3. At Focal point F At infinity Real, inverted and enlarged 4. Between C and F Beyond C Real, inverted and enlarged 5. At C At C Real, inverted and of the same size as the object 6. Beyond C Between F and C Real, inverted and diminished Q. Is it inverted or erect, enlarged or diminished ?    A. See in the table above column 3 nature of the image for all types of images formed.

14 (T.S.) PHYSICAL SCIENCE – Class 10 Q. What do you infer from the above table ?    A. From the above table, we can infer that images formed at different positions have different focal point, size and nature of image. Q. Why only at point A?    A. If we hold the screen at any points before or beyond point A, we see that the rays will meet the screen at different points. Therefore the images of the tip of the flame will be formed at different points due to the rays. If we draw more rays emanating from the same tip we will see that at point A. They do not meet at point ‘B’ Q. Where is the base of the candle expected to be in the image when the candle is placed on the axis of the mirror?    A. The base of the candle is expected to be on the principal axis in the image when the object is placed on the axis of the mirror. Q. During the experiment did you get any positions where you could not get an image on the screen?    A. Yes, we do not get an image on the screen when the object (O) is placed at a distance less than the focal length of the mirror. Think and Discuss Q. Do you get an image when the object is placed at F ?    Draw a ray diagram. Do the experiment. A. 1) Yes, we get an image at infinity when the object is placed at F. 2) Ray diagram for the object and image formed is drawn below : C FP EXPERIMENT : After performing the experiment, the results are as follows : RESULT : 1) Object at focus (F) image at Infinity. 2) Nature : Real, inverted and enlarged. Remember • When light rays shine on a smooth metal surface they are reflected in a way that produces a clear image. This is called specular reflection. • You can see your own reflection in a mirror. The image that you see is very clear because the light rays bounce off the smooth mirror in a precise way. • When light shines on a rough surface the rays are reflected at many different angles and the image becomes distorted. This is called diffuse reflection.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 15 TOPICWISE EXAMINATION PATTERN QUESTIONS & ANSWERS Reflection of Light by Spherical Mirrors : (2 Marks) 1. What are laws of reflection of light ? Explain. (OR) State the laws of reflection.(2 Marks) Ans. Laws of Reflection of Light : When light undergoes reflection from a smooth polished surface, it obeys two laws which are known as the “Laws of reflection of light”.  First law : The first law states that, “The incident ray, the reflected ray and the normal at the points of incidence all lie in the same plane.”  Second law : The second law states that, “The angle of incidence is equal to the angle of reflection i.e., ∠i = ∠r.” These laws of reflection are applicable to all types of reflecting surfaces including spherical surfaces. 2. What is reflection ? Explain with an example how rays are distributed. ( 2 Marks) Ans. 1) Reflection is the phenomenon of bouncing back of the rays of light when they fall on an obstacle. 2) Example : It is similar to the bouncing of a ball when we throw it on a rigid surface. 3) When light rays fall on an object, some of them are reflected, some pass through it and the rest of the light rays are absorbed by the object. 3. How can we distinguish between a plane mirror, a convex mirror and a concave mirror? (2Marks) Ans. We can distinguish between a plane mirror, a concave mirror, and a convex mirror by bringing our face close to each mirror, turn by turn. 1) If the image is of the same size as our face, it is a plane mirror. ... 2) If the image is magnified, it is a concave mirror. 3) If the image is diminished, it is a convex mirror. 4. What are concave and convex mirrors? Distinguish them. ( 2 Marks) A ns. 1) Concave and convex mirrors are the types of spherical mirrors.Concave mirrors have an inward curvature in the centre and reflect light inward to focus it on a single focal point. 2) Concave mirrors provide a variety of images depending on the distance between the mirror and the item. 3) Convex mirrors have an outward bulge in the center that allows light to fall directly on the item. It’s also known as a diverging mirror since it can diverge the rays that fall on its surface after reflection. This is a reference to the fact that parallel rays diverge when they touch the reflected surface of a convex mirror. 5. What are the 3 main differences between a convex and concave mirror?(AS1) ( 2 Marks) Ans. The following are the three differences between concave and convex mirrors: 1) A concave mirror is a spherical mirror with an inwardly curved reflection surface, whereas a convex mirror is a spherical mirror with an outwardly bulged reflecting surface. 2) A concave mirror has a converging character and is so-referred to as a converging mirror, whereas a convex mirror has a diverging nature and is thus referred to as a diverging mirror.

16 (T.S.) PHYSICAL SCIENCE – Class 10 3) The focal length of the concave mirror is negative and the focal length of the convex mirror is positive. 6. What is the difference between concave and convex mirrors in terms of : 1) physical appearance 2) focal length 3) type ( 2 Marks) Ans. 1) Physical appearance : A concave mirror has an inward curvature in the centre whereas Convex mirrors have an outward bulge in the center. 2) Focal length : The focal length of the concave mirror is negative because the focus is on the front side, but the focal length of the convex mirror is positive because the focus is on the backside. 3) Type : Concave mirrors are converging mirrors, whereas convex mirrors are diverging mirrors. 7. Distinguish between real and virtual images formed in concave and convex mirrors. (AS1) A ns. 1) A real image is formed by a concave mirror whereas a virtual image is formed by a convex mirror. 2) A real image can be obtained on a screen, whereas a virtual image cannot be obtained on a screen but it can be seen. 3) A real image may be enlarged or diminished but a virtual image is always diminished. 4) A real image is always inverted and is formed on the same side of the mirror. But a virtual image is always erect and is formed on the other side(back) of the mirror. 8. Write the aim, objective and materials required for conductiong an experiment to measure the object distance and image distance from the mirror. ( 2 Marks) Ans. 1) Aim : To to find the types of images formed and measure the object distance and image distance from the mirror. 2) Materials required : a) A candle b) Paper c) Concave mirror d) V-stand e) Measuring tape 9. What do you know about the terms given below related to spherical mirrors ? ( 2 Marks) a) Pole b) Centre of curvature (AS1) A ns. a) Pole : 1) The mid point or geometrical centre of the reflecting surface of a spherical mirror is called pole of the mirror. It is denoted by the letter (P). 2) It is the lowest point in case of the concave mirror and the highest point in case of the convex mirror. All distances are measured from the pole of the mirror. Ans. b) Centre of curvature : 1) The geometrical centre of the hollow sphere of which the spherical mirror is a part is called the centre of curvature (C). 2) It is denoted by the letter (C) and lies outside the surface of the mirror. 10. Explain the terms given below related to spherical mirrors ? (AS1) ( 2 Marks) ir Angle of reflection Angle of incidence 1) Focus 2) Radius of curvature O Point of incidence Ans. 1) Focus (Principal Focus) (F) :

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 17 The focus is also known as principal focus (F) of a spherical mirror. It is the point on the principal axis where all rays of light incident on the mirror, parallel to the principal axis, meet (in case of concave mirror) or appear to meet after reflection (in case of convex mirror). A ns. 2) Radius of Curvature : 1) The distance between the pole (P) and the centre of curvature (C) of the mirror is called the radius of curvature. 2) It is denoted by (R). R = 2f . 11. What do you mean by : a) Focal length b) Principal axis (AS1) ( 2 Marks) a) Focal length (f) : A ns. 1) The distance between the Pole and the Principal focus of the mirror is called the focal length ( f ) of the spherical mirror. It is represented by the symbol ( f ). 2) For a concave mirror focal length is negative (–ve) and for convex lens it is positive (+ve). The relation between focal length ( f ) and radius of curvature (R) is same for both the types of mirrors and is given by f = R. 2 b) Principal axis : A ns. The imaginary horizontal straight line which passes through the centre of curvature and pole of the mirror is called principle axis of the mirror. 12. What do you mean by : (AS1) ( 2 Marks) 1) Object distance 2) Image distance 3) Magnification Ans. 1) Object distance : The distance of the object from the pole of the mirror is called as object distance (u). 2) Image distance : i) The distance of the image from the pole of the mirror is called image distance (v). ii) This distance is positive for real images and negative for virtual images. 3) Magnification : i) Magnification of a spherical mirror is defined as “the ratio of the size of the image (hi) as formed after reflection from the mirror to the size of the object (ho)”. ii) It is denoted by the symbol (m). 13. How can you identify the three types of mirrors without touching them ? ( 2 Marks) Ans. We will look into the mirror by going close to it: i) If image is of same size and erect it is a plane mirror. ii) If image is of bigger size and erect it is a concave mirror. iii) If image is of smaller size and erect it is a convex mirror. 14. What are the characteristics of the image formed in a plane mirror? ( 2 Marks) Ans. 1) The image is laterally inverted. 2) The image is erect. 3) The size of the image is the same as the size of the object. 4) The distance between the image obtained from the mirror is the same as the distance between the object from the mirror. 15. A wall reflects light and a mirror also reflects light. What difference is there in the way they reflect light? ( 2 Marks) Ans. 1) The difference between reflection of light from wall and mirror is that the reflection from wall is a diffuse reflection as it has rough surfaces.

18 (T.S.) PHYSICAL SCIENCE – Class 10 2) A parallel beam of light incident on it is reflected in different directions i.e., get scattered in different directions. 3) Whereas by a mirror it is a regular reflection as mirror surface is smooth. 4) A parallel beam of light incident on it gets rays reflected in regular(one) direction. 16. State and explain the laws of reflection of light at a plane surface (like a plane),with the help of a labeled ray-diagram. Mark the angles of ‘incidence’,‘reflection’ and the point of incidence clearly on the diagram. If the angle of relection is 45°, what will be the angle of incidence? ( 2 Marks) Ans. Laws of reflection of light: 1) First law of reflection: This law states that incidence ray, the relected ray and the normal(at the point of incidence), all lie in the same plane. For e.g : in the figure, the incident ray, the reflected ray and the normal, all lie in the same plane, the plane of paper. 2) Second law of reflection: This law states that angle of reflection is always equal to the angle of incidence. For e.g : If angle of reflection is 45°, then the angle of incidence will also be 45°. 17. What is the relation between the focal length and radius of curvature of a spherical mirror (concave mirror or convex mirror)? Calculate the focal length of a spherical mirror whose radius of curvature is 26 cm. ( 2 Marks) Ans. For a spherical mirror the principal focus (F) lies exactly mid-way between the pole (P) and centre of curvature (C). So, the relation between focal length(f) of a spherical mirror and radius of curvature (R) is f = R/2. The focal length of a spherical mirror is equal to half of its radius of curvature or The radius of curvature is twice the focal length (R) = 2f Radius of curvature (R) = 26cm Focal length (f) = ? We know that f = R/2 f = 26/2 f = 13cm 18. State the relation between object distance, image distance and focal length of a spherical mirror (concave mirror or convex mirror). ( 2 Marks) Ans. 1/v + 1/u = I/f Or 1/Image distance + 1/Object distance = 1/Focal length where, v = distance of image from mirror u = distance of object from mirror f = focal lenth of the mirror 19. What would your image look like if you stood close to a large : (a) convex mirror? (b) concave mirror ? Give reasons for your answer. ( 2 Marks) Ans. (a) Our image will be diminished, virtual and erect if we stand close to a large convex mirror because when the object lies anywhere between the pole and iniinity, the concave mirror forms a diminished, virtual and erect image. (b) Image will be enlarged, virtual and erect if we stand close to a large concave mirror because when the object lies within the focus of a concave mirror, it forms an enlarged, virtual and erect image.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 19 20. The shiny outer surface of a hollow sphere of aluminium of radius 60cm is to be used as a mirror : ( 2 Marks) (a) What will be the focal length of this mirror? (b) Which type of spherical mirror will it provide ? (c) State whether this spherical mirror will diverge or converge light rays. Ans. a) R = 60cm f = ? We know that f = R/2 = 60/2 = 30 cm (b) It will provide convex mirror. (c) diverge light rays. Ray diagrams for Concave mirror & Convex mirrors : (2 Marks) 1. Draw images of an incident ray passing through the Centre of Curvature (C) of 1) Concave mirror 2) Convex mirror and explain their paths. ( 2 Marks) Ans. 1) Concave mirror: CF P Explanation : An incident ray passing through the centre of curvature of a concave mirror reflects back along the same path, without any deviation. 2) Convex mirror : P FC Explanation : In case of a convex mirror, an incident ray which appears to move towards the direction of centre of curvature is reflected back in the same path without any deviation. 2. Draw images of an incident ray parallel to the principal axis of 1) Concave mirror 2) Convex mirror and explain their path. ( 2 Marks) Ans. 1) Concave mirror: CF P Explanation : In case of a concave mirror, an incident ray parallel to the principal axis passes through the focus after reflection. 2) Convex mirror : P FC Explanation : In case of a convex mirror, the incident ray passing parallel to principal axis, after reflection appears to come from the focus of the mirror.

20 (T.S.) PHYSICAL SCIENCE – Class 10 3. Draw images of an incident ray passing therough the focus of 1) Concave mirror 2) Convex mirror and explain their path. ( 2 Marks) Ans. 1) Concave mirror: CF P Explanation :In a concave mirror, an incident ray passing through the focus is reflected parallel to the principal axis. P FC Explanation : In case of a convex mirror, the incident ray after reflection appears to come from the focus of the mirror and is reflected parallel to the principal axis. 4. Draw images of an incident ray passing therough the focus of 1) Concave mirror 2) Convex mirror and explain their path. ( 2 Marks) Ans. 1) Concave mirror: CF i rP Explanation : In a concave mirror, a ray of light incident at the pole gets reflected along a path such that the angle of incidence is equal to the angle of reflection ∠i = ∠r. i C FrP Explanation : This is also true for a convex mirror ∠i = ∠r. 5. While drawing ray diagrams we follow certain rules of reflection for placement of objects using concave mirrors. What are they : Explain with a diagram. ( 2 Marks) Ans. To draw ray diagrams, we have to follow the rules of reflection for concave mirrors as follows : object LEFT Right O Principal axis reflecting surface Placement of object while drawing a ray diagram : Ray diagrams: While drawing ray diagrams, the important rules regarding the placement of the object are as follows : 1) The reflecting surface must face towards the left side. 2) The object(O) must be kept perpendicular to the principal axis such that its foot touches it.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 21 6. Identify the diagram and write its characteristics. ( 2 Marks) B B' D C FA P A' Ans. 1) It is identified as a concave mirror. 2) The object id placed between F and P. 3) Image is formed ehind the mirror. 4) Nature and size of the image : It is Virtual, Enlarged and Erect. 7. Observe this figure and i) identify the mirror ii) redraw the diagram and show the direction of the light ray after reflection: ( 2 Marks) PF C Ans. 1) It is identified as Convex mirror. 2) Redrawn diagram : P FC 8. How do you get a virtual, enlarged image using a concave mirror ? Is there any other position of object using a concave mirror to get a virtual enlarged image ?. ( 2 Marks) Ans. We can get a virtual image of an object in the following way : 1) Place an object between pole (P) and focus (F) of the concave mirror. 2) The image formed will be virtual, erect, enlarged, and behind the mirror. 3) Explanation / Reason : This is because, the two reflected rays do not meet in front of the mirror. They appear to meet behind the mirror when extended backwards. Thus, the image formed is virtual image . 4) No. This is the only position of the object placed before the concave mirror to get an virtual, enlarged image. Other positions of the object forms real images or images at infinity. 9. What is the minimum number of rays required for locating the image formed by a concave mirror for an object? Draw a ray diagram to show the formationof a virtual image by a concave mirror. ( 2 Marks) A ns. Minimum two rays are required.

22 (T.S.) PHYSICAL SCIENCE – Class 10 B' B D C FA P A' Ray diagram for the formation of a virtual image by a concave mirror: 10. If an object is placed at a distance of 8 cm from a concave mirror of focallength 10 cm, discuss the nature of the image formed by drawing the ray diagram. ( 2 Marks) Ans. B' B D C FA P A' The focal length of the mirror is PF = 10 cm. The object is placed at A B such that object distance, PB = 8 cm. This means that the object lies between the pole and focus of the concave mirror. Nature of the image : The image formed is virtual, erect and magniied behind the mirror. 11. Where will the image be formed when we place an object on the principal axis of a concave mirror at a point between focus (F) and centre of curvature (C). ( 2 Marks) Ans. The image (I) will be formed beyond the centre I O of curvature (C). C F Nature of the image : The image will be real, inverted and magnified. Sign convention : u, v and f are all negative (–ve). 12. A ray of light is incident on a convex mirror as shown in the diagram . Redraw the diagram and complete the path of these rays after reflection from the mirror. Mark angle of incidence and angle of reflection on it. Also draw figure for concave mirror. ( 2 Marks) P FC Ans. r i i r FC Concave mirror Convex mirror

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 23 13. Under what condition in an arrangement of two plane mirrors, incident ray and reflected ray will always be parallel to each other, whatever may be the angle of incidence. Show Ans. the same with the help of diagram. ( 2 Marks) i r ir 14. List out four specific characteristics of the images of the objects formed by convex mirrors. Ans. 1) Image is always formed behind the mirror, between the pole and its focus. ( 2 Marks) 2) The image is always virtual and erect. 3) The size of image is always small than the object. 4) Magnification is always positive. 15. Observe the diagram and write what do you mean by : R ( 2 Marks) 1) (P) 2) the horizontal line passing through the centre i r of curvature and pole 3) the distance between P and C of the mirror. and CP 4) i and r A ns. 1) (P) Pole of the mirror 2) Principal axis 3) Radius of curvature (R) 4) i = angle of incidence and r = angle of reflection. 16. List two properties of the images formed by convex mirrors. Draw a ray diagram in support of your answer. ( 2 Marks) A ns. Properties : X A convex lens always forms : AD 1) a virtual and erect image. A' E 2) an image smaller than the object. B P B' F C Object Image M 17. Draw a diagram showing pole, centre of curvature, principal axis of a spherical mirror. ( 2 Marks) Ans. Principal axis C- P-Pole Centre of curvature

24 (T.S.) PHYSICAL SCIENCE – Class 10 18. Draw the ray diagram to show the formation of image for the object of height 1 cm. placed at 5 cm. distance, in front of a convex mirror having the radius of curvature R = 5 cm.(2M) Ans. Ray diagram for the given data : 1 cm CF 5 cm 5 cm u 19. Write the characteristics of the image formed by a concave mirror when an object is placed. Between F and C. ( 2 Marks) Ans. Characteristics of the image : J When an object (OJ ) is placed at a point between F and C the following characteristics are noticed : Position of the image : The image (G) is formed CO F P beyond the centre of the curvature (C). G Nature and size of the image : It is real, inverted and magnified. 20. Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that its image formed is equal to the size of the object ? ( 2 Marks) Ans. 1) As we know that for concave mirror, if object is placed at infinity, its image will be formed at focus. 2) Thus, from the question, focal length of the given mirror will be 15 cm. And for same size of image , in case of concave mirror object must be placed at centre of curvature (C). R = 2f R = 2 x 15 = 30 cm. 21. Observe the diagram and show the formation of image of the object AB with the help of suitable rays. ( 2 Marks) A C BF Ans. According to given figure, the object is between C and F so the image will be formed beyond C. Hence the figure will be as follows : B' A D C BF P A' E

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 25 22. By observing steel vessels and different images in them, Vijay a third class student, asked his elder sister Nivedita some questions. What may be those questions? ( 2 Marks) Ans. 1) Why do our image appears to be small and big in size ? 2) Why some images appear to be inverted, and some appear to be erect ? Can the similar images be caught on the wall ? 3) Why do lustrous vessels give more sharp images then the old ones ? 4) If we see our face in a dome shaped vessel how would your image look from the outer surface and inner surface of the vessel ? 22. How can we show how the size and nature of image of an object change when it moves from centre of curvature of concave mirror towards the pole of the mirror. ( 2 Marks) Ans. It can be shown in the following ways : 1) When the object is placed at the centre of curvature, the image formed is real, inverted and of the same size 2) When the object is placed between the centre of curvature and focus, the image formed is real, inverted and enlarged 3) When the object is placed between the focus and pole the image formed is virtual, erect and enlarged. 23. Draw a ray diagram showing position of an object at infinity and write the details of position of the image formed and nature & size of image formed. ( 2 Marks) Ans. Ray Diagram : Position of Object : At infinity (∞) Position of Image : At Focus(F) B P F Nature and size of Image : Real, inverted & highly diminished. A 24. Draw a ray diagram showing position of an object beyond C and write the details of position of the image formed and nature & size of image formed. Ans. Ray Diagram : A' Position of Object : Beyond C Position of Image : Between f & C : B P CF B' A Nature and size of Image : Real, inverted & diminished 25. Draw a ray diagram showing position of an object at C and write the details of position of the image formed and nature & size of image formed. Ans. Ray Diagram : BD Position of Object : At C A F P Position of Image : At C A' C Nature and size of Image : Real, inverted & same size B' E 26. Draw a ray diagram showing position of an object between f & C and write the details of position of the image formed and nature & size of image formed. Ans. Ray Diagram : A F D Position of Object: Between f & C B' Position of Image : Beyond C P Nature and size of Image: Real, inverted & enlarged CB E A'

26 (T.S.) PHYSICAL SCIENCE – Class 10 27. Draw a ray diagram showing position of an object at f and write the details of position of the image formed and nature & size of image formed . Ans. Ray Diagram : Position of Object : At F C B Position of Image : At infinity Nature and size of Image : Real, inverted & highly enlarged A FP 28. Draw a ray diagram showing position of an object between f & P and write the details of position of the image formed and nature & size of image formed. ( 2 Marks) Ans. Ray Diagram : B' Position of Object: Between f & P B D Position of Image : Behind the mirror C FA P A' Nature and size of Image: Virtual, enlarged and erect image 29. Draw a ray diagram of convex mirror showing position of an object at infinity and write the details of position of the image formed and nature & size of image formed. ( 2 Marks) Ans. Ray Diagram : M Position of the object : At infinity ∞ A Position of the images : At focus (F) behind the mirror PF C N Nature of the images : Virtual, erect and highly B diminished At infinity 20. Draw a ray diagram of convex mirror showing position of an object at infinity and write the details of position of the image formed and nature & size of image formed. ( 2 Marks) Ans. Ray Diagram : X Position of the object : Between ∞ and pole of the A D C mirror. B E A' Position of the images : Between P & F behind the Object mirror. P B' F Image Nature of the images : Virtual, erect and diminished Derivation of formula for curved mirrors : (2 Marks) M 1. What is mirror formula? How do you solve mirror formula problems? ( 2 Marks) A ns. The relationship between object distance (u), the image distance (v) and the focal length (f) of the mirror is known as the mirror formula. The problems related to mirror formula will be solved in the following steps : 1) If object is at left side of the mirror the object distance is taken as negative. 2) If it is in right side of the mirror it is taken as positive. 3) Formula : 1 = 1 + 1 f u v 2. An object is kept 60cm in front of a concave mirror of focal length 30cm. Find the position of the image formed. ( 2 Marks) Ans. Given that, The object distance is u = –60cm The focal length of the concave mirror is f = –30cm

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 27 The image distance is given by the relation, v1 = 1 - 1 = 1 - 1 f u 30 60 \\ 1 = -1 + 1 = -2+1 = -1 v 30 60 60 60 \\ v = – 60cm Hence, the image is formed in front of the concave mirror at a distance of 60cm. 3. A convex mirror used for rearview on the bus has a radius of curvature of 4m. If a car is located at 2m from the mirror, find the position of the image. ( 2 Marks) Ans. Given that, The object distance is u = –2m The radius of curvature of the convex mirror is R = 4m R 4 So, the focal length of the convex mirror is f = 2 = 2 = 2m The image distance is given by the relation, v1 = 1 - 1 = 1 - 1 f u 2 -2 \\ 1v = 1 + 1 = 2 = 1 2 2 2 1 \\ v = 1m Hence, the image of the car is formed behind the mirror at a distance of 1m. 4. Find out the focal length with sign in case of concave mirror with a radius of curvature 20 cm. ( 2 Marks) Ans. As we know that R = 2f Where R = radius of curvature of concave mirror, f = focal length of concave mirror R = 2f \\ f = R 2 \\ f= 20 2 f = -10cm (negative indicates that it is a concave mirror.) Hence, the focal length of the concave mirror is 10 cm. 5. What is the image distance in case of concave mirror if the object distance is 16 cm? It is given that the focal length of the mirror is 8 cm. ( 2 Marks) Ans. As we know from mirror formula, 1f = 1 + 1 v u Where u = object distance = -16cm v = image distance = ? f = focal length of mirror= -8cm Putting values we get v1 = 1 - 1 -8 -16

28 (T.S.) PHYSICAL SCIENCE – Class 10 v1 = 1 + 1 -8 16 1v = -2 + 1 16 16 1v = -1 16 v = -16 cm Hence the object is located 16 cm in front of the mirror. Sign convention for the parameters related to the mirror equation: (2 Marks) 1. Define the new Cartesian sign conventions and write any two rules.. ( 2 Marks) Ans. Definition : The set of rules, to use ‘+’ or ‘–’ sign with the values while solving any problems in optics is called sign convention. They are : 1) The object is always placed to the left of the mirror, so that incident light moves left to right. 2) All distances are to be measured from the pole of the mirror i.e., from origin of coordinate axis. 2. Write any four new Cartesian sign conventions which we follow while solving problems related to mirrors. ( 2 Marks) Ans. New Cartesian sign conventions : 1) The object is always placed to the left of the mirror, so that incident light moves left to right. 2) All distances are to be measured from the pole of the mirror i.e., from origin of coordinate axis. 3) The distances measured in the direction of the incident light will be taken as +ve, and those measured in the direction opposite to incident light will be taken as –ve. 4) All measured of height above the principal axis are to be taken as positive (+ve) and below are taken as negative (– ve). 3. Diagrammatically explain Cartesian sign conventions. ( 2 Marks) Ans. Diagrammatic Explanation of Cartesian sign conventions : Object on the left Direction of incident light MY A Distance along incident light (+ve) Height Pole P upwards Distance against incident light (–ve) N Positive (+ve) B' Y' X' B F X Height Mirror downwards A' Negative (–ve) 4. What is the sign convention to be taken while solving problems related to image or object distance in case of concave mirrors?

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 29 Ans. For Concave Mirror 1) The object is always kept in front of the concave mirror and its distance from the mirror is taken as negative. 2) The center of curvature and focus lie in front of the concave mirror, therefore radius of curvature and focal length are also taken as negative. 3) Image height is taken as positive in the case of erect image and taken as negative in the case of an inverted image. 4) The real image is formed in front of the mirror, therefore, the image distance is taken as negative and for virtual image, it is taken as positive which is formed behind the mirror. 5. What is the sign convention to be taken while solving problems related to image or object distance in case of convex mirrors? ( 2 Marks) Ans. For Convex Mirror : 1) The object is always kept in front of the convex mirror and its distance from the mirror is taken as negative. 2) The center of curvature and focus lie in behind of the convex mirror, therefore radius of curvature and focal length are also taken as positive. 3) In a convex mirror, an image formed is always erect, thus the image height is taken as positive. 4) In a convex mirror, the image formed is always behind the mirror, therefore the image distance is taken as positive. Magnification (m) : (2 Marks) 1. What do you mean by magnification? Write its formula. ( 2 Marks) Ans. 1) Magnification : Magnification of a spherical mirror is defined as “the ratio of the size of the image (hi) as formed after reflection from the mirror to the size of the object (ho)”. 2) It is denoted by the symbol (m) 3) Formula for Magnification : m = size of the image  hi  or m = − v  size of the object  ho  u    Where, v = image distance, u = object distance 2. The magnification of the image by the concave mirror is -1. Mention the four characteristics of image from the above information. ( 2 Marks) A ns. The four characteristics of the image formed are : 1) real 2) inverted 3) same size as the object and 4) behind the mirror. Note :( A magnification of 1 (plus or minus) means that the image is of the same size as the object). 3. The magnification produced by a mirror is +1. What does it mean? (AS1) ( 2 Marks) A ns. 1) Magnification (m) is defined as the ratio of the size of the image (hi) to the size of the object (ho). It is calculated by using the formula given below : Magnification (m) = size of the image  hi  size of the object  ho    2) The magnification produced by a plane mirror is +1 implies that the image formed by a plane mirror is virtual, erect and of the same size as that of the object.

30 (T.S.) PHYSICAL SCIENCE – Class 10 4. List two possible ways in which a concave mirror can produce a magnified image of the object placed in front of it ? State the difference, if any, between these two images. ( 2 M) Ans. 1) A concave mirror can produce a magnified image of an object when it is placed : i) within its pole and its focus ii) between F and C 2) Difference between two images : The image produced in first case will be virtual and erect. The image produced in the second case will be real and inverted. M aking of Solar Cooker : (2 Marks) 1. Write the procedure to make a solar cooker. ( 2 Marks) Ans. 1) Make an wooden/iron frame in the shape of TV dish. 2) Cut acrylic mirror sheets into 8 - 12 pieces in the shape of isosceles triangles with a height equal to the radius of your dish antenna. 3) The bases of 8 - 12 triangles together makes the circumference of the dish. 4) Stick the triangle mirrors to the dish as shown in figure. Your solar heater cooker is ready. 5) Arrange it so that concave part faces sun. Find its focal point and place a vessel at that point. The vessel gets heated enough to cook rice. A pplications of Concave & Convex mirrors : (2 Marks) 1. Write any six uses of concave mirrors. ( 2 Marks) Ans. Uses of concave mirrors: It is used as/in/by 1) shaving mirror. 2) a reflector to concentrate light in solar cookers. 3) reflecting type astronomical telescope. 4) search light, head light of automobiles etc. 5) dentists to observe cavities in the teeth. 6) ophthalmoscope, to examine eye, nose throat and ear of a person. 2. Write any four uses of convex mirrors. ( 2 Marks) Ans. Uses of convex mirrors : It is used : 1) as a rear view mirrors in automobiles. 2) as a device to check theft in shops. 3) to bring view of corners which are not directly accessible. 4) to light a large area. 3. Why concex mirrors are preferred more than concave mirrors in vehicles ? ( 2 Marks) Ans. 1. Convex mirrors are preferred more because they : a) gives a wider field of view as the mirror is curved outward. b) produces erect and diminished image of the traffic behind the driver of the vehicle. 2. Thus, convex mirrors enable the driver to view much larger area than would be possible with a plane mirror.

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 31 4. Give two uses of concave mirrors. Explain why you would choose concave mirrors for these uses. ( 2 Marks) Ans. Uses of concave mirror 1) Concave mirrors are used by dentists. Since the tooth looks much bigger through concave mirror hence it becomes easy to examine the defect in the tooth 2) Concave mirrors are used as shaving mirrors as when the face is placed close to a concave mirror the concave mirror produces a magniied and erect image of the face so that it becomes easier to make a smooth shave. 5. Identify the type of mirror used in the following : ( 2 Marks) 1) Vehicle mirrors 2) Headlight of motor cycle 3) Spoon surface (back side) 4) Spoon surface (front side) A ns. 1) V ehicle mirrors Convex Mirror 2) Headlight of motor cycle Convex Mirror 3) S poon surface (back side) Convex Mirror 4) S poon surface (front side) Concave Mirror 6. In a trick mirror the image of the head appears much smaller than that of the mouth and of nose. Explain why ? ( 2 Marks) A ns. 1) A trick mirror is basically a concave mirror having small focal length. 2) The head is comparatively away from the nose and mouth. So the magnification is smaller than that of nose and mouth. This is the reason that nose and mouth appear to be larger in size than the head. 7. Give reasons : ( 2 Marks) 1. Concave mirrors are commonly used in torches, search-lights and vehicles headlights. 2. They are often used as shaving mirrors and by dentists. 3. Large concave mirrors are used to concentrate sunlight in solar furnaces. Ans. 1. Concave mirrors are commonly used in torches, search-lights and vehicles headlights to get powerful parallel beams of light. 2. They are often used as shaving mirrors to see a larger image of the face. The dentists use concave mirrors to see large images of the teeth of patients. 3. Large concave mirrors are used to concentrate sunlight to produce heat in solar furnaces. 8. A wall reflects light and a mirror also reflects light. What difference is there in the way they reflect light ? Ans. 1) A wall has a rough surface, so the reflection by a wall is a diffuse reflection. 2) A parallel beam of light incident on it is reflected in different directions. 3) A mirror surface is smooth, so the reflection by a mirror is a regular reflection. 4) A parallel beam of light incident on it, gets scattered by making reflected rays in different directions.difference-there-they-reflect-light

32 (T.S.) PHYSICAL SCIENCE – Class 10 MCQs MULTIPLE  CHOICE  QUESTIONS 1Mark Choose correct option (A, B, C, D) and write in the given bracket Time : 15 Minutes Max. Marks : 10 Instructions: 1. Answer all the questions. 2. Each question carries 1 mark . 3. In this section there are four options(A, B, C, D) to each question. Choose the appropriate answer ansd write the answer in the brackets given against the question. 4. Part - B must be attached to the answer booklet of Part - A. 1. Consider the diagram below. Which one of the angles (A, B, C, or D) is the angle of incidence? Which one of the angles is the angle of reflection? Choose the correct statement (sentence). [] BC AD Mirror A) Angle B is the angle of incidence. Angle C is the angle of reflection. B) Angle A is the angle of incidence. Angle D is the angle of reflection. C) Angle A is the angle of incidence. Angle C is the angle of reflection. D) Angle B is the angle of incidence. Angle D is the angle of reflection. 2. Choose the correct statement (sentence) : [] The image of an object formed by a plane mirror is: A) Virtual, behind the mirror and enlarged. B) Real, at the surface of the mirror and enlarged. C) Virtual, behind the mirror and of the same size as the object. D) Real, behind the mirror and of the same size as the object 3. The figure given alongside shows the image of a clock as seen in a plane mirror. The correct time is: [] 21 39 6 A) 9.25 B) 2.35 C) 6.45 D) 2.25

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 33 4. In a convex spherical mirror, reflection of light takes place at: [] A) A bulging-out surface B. A bent-in surface C. A lat surface D. An uneven surface Ans. A is correct 5. The focal length of a spherical mirror of radius of curvature 38 cm is: [] A) 10 cm B) 19 cm C) 20 cm D) 30 cm 6. The real image formed by a concave mirror is larger than the object when the object is : A) between focus and centre of curvature. [] B) distance less than the focal length. C) curvature at a distance equal to radius of curvature D) at a distance greater than radius of curvature 7. Match the following : [] Column - I ` Column - II a) Object At infinity (1) Image at infinity b) Between P and F (2) Image behind the mirror c) At Focal point F (3) Image beyond C d) Between C and F (4) Image at F A) a-4, b) b-2, c-1, d-3 B) a-2, b) b-1, c-3, d-4 C) a-3, b) b-1, c-4, d-2 D) a-4, b) b-3, c-1, d-2 8. Formula used to find the magnification is : [] i) m = -v ii) m = v u u iii) m = hi iv) m= ho ho hi A) i and iii B) i and iv C) iii and iv D) iv and ii 9. Convex mirror is used to form an image of the object. Which of the following statements is wrong? [] A) The image is erect B) The image is diminished in size C) The image is real D) The image lies between the pole and the focus

34 (T.S.) PHYSICAL SCIENCE – Class 10 10. A spherical mirror and a spherical lens each have a focal length of -10 cm. The mirror and the lens are likely to be [] A) concave B) convex C) the mirror is concave and the lens is convex D) the mirror is convex and the lens is concave 11. A point object is placed at a distance of 20 cm from a convex mirror of focal length 20 cm. The image will form at: [] A) at infinity B) at focus C) at the pole D) behind the mirror 12. Choose the correct pair : [] A) Object at C, Image at C. [] B) Object at F, Image at F. C) Object beyond C, Image at P. D) Object at P, Image at C. 13. Choose the incorrect pair : A) Object at infinity, Image at F. B) Object between P & F, Image behind the mirror. C) Object between C & F, Image beyond C. D) Object at P, Image at C. 14. Choose the incorrect statement(sentence) : [] A) If object is placed at infinity, the image is formed at F. B) If object is placed between P & F, the image is formed behind the mirror. C) If object is placed between C & F, the image is formed beyond C. D) If object is placed at P, the image formed is at C. 15. Select the missing label of the diagram : [] Angle of incidence ir Angle of reflection O ? A) incidence B) reflection C) Point of incedence D) Point of reflection

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 35 ANSWERS TO MCQs 1) Answer (B) is correct : Angle A is the angle of incidence. Angle D is the angle of reflection. Explanation/Reason : Angel of incidence always lie between the Incident ray and normal so angle A is the correct answer. Similarly angle of reflection lies between the Reflected ray and normal so angle D is the correct answer. 2) Answer (C) is correct : Virtual, behind the mirror and of the same size as the object.. Explanation/Reason : A plane mirror is a mirror in which a reflecting surface is a plane. The image formed by a plane mirror is virtual, behind the mirror, and of the same size as the object. The distance of the image from the mirror is the same as the distance of the object from the mirror. C is the corect answer. 3) Answer (A) is correct : 9.25. Explanation/Reason : When an object is placed in front of a plane mirror, then the right side of the object appears to become the left side of the image; and the left side of the object appears to become right side of the image. This change of the sides of an object and its mirror image is called lateral inversion.. So A is the correct answer. 4) Answer (A) is correct : A bulging-out surface. Explanation/Reason : A spherical mirror whose inner side is silvered(polished) and outer bulging side is the reflecting surface. When a ray strikes the outer bulging surface get reflected. 5) Answer (B) is correct : 19 cm. Explanation/Reason : The focal length of a spherical mirror is equal to half of its radius of curvature (both convex as well as concave mirror). (O R ) The radius of curvature is twice the focal length (R) = 2f Mathematically, Focal length = Radius of curvature or f = R or R = 2f 2 2 Focal length of a spherical mirror is f= R . Therefore f= 38 = 19cm. 2 2 6) Answer (A) is correct : Between focus and centre of curvature.. Explanation/Reason : For an object placed between the focus (f) and the centre of curvature (c), the image formed will be real and larger than the object. 7) Answer (A) is correct : a-4, b) b-2, c-1, d-3. Explanation/Reason : When the Object is at infinity, the image formed will be at F. W hen the Object is between P and F, the image formed will be behind the mirror. When the Object is at focal point F, the image formed will be at infinity. When the Object is between C and F, the image formed will be beyond F. 8) Answer (A) is correct : i) m = -v , iii) lmine=arhhmoi .agnification u Explanation/Reason : Magnification or may be defined as “the ratio of the size of the image (hi) to the size of the object (ho)”. It is denoted by m. • The magnification (m), produced by a spherical mirror can be expressed as : m = Height of the image (hi) =  hi  = − v  on applying sign convention. Height of the object (ho)  ho  u    • Magnification is also equal to the ratio of image distance to the object distance. − v  u 

36 (T.S.) PHYSICAL SCIENCE – Class 10 9) Answer (C) is incorrect : The image is real. Explanation/Reason : Convex mirror always produces a virtual image. It cannot produce a real image. So, the image formed by a convex mirror is virtual, erect and highly diminished or diminished image only. So the anser C is correct. 10) Answer (A) is correct : Concave. Explanation/Reason : Here, the focal length is given with a negative sign(-10), and both the concave lens and the concave mirror has a negative focal length. So the anser A is correct. 11) Answer (D) is correct : Behind the mirror. Explanation/Reason : The image is formed behind the mirror (due to the positive image distance). 12) Answer (A) is correct : A) Object at C, Image at C. Explanation/Reason : Concave mirror forms image of the object placed at C, at the C itself but inverted, real and of the same size. 13) Answer (D) is incorrect : Object at P, Image at C. Explanation/Reason : When an object is placed at C an image is formed at C only, it cannot be P. So, the anser D is incorrect. 14) Answer (D) is incorrect : If object is placed at P, the image formed is at C.. Explanation/Reason : When an object is placed at C an image is formed at C only, it cannot be P. So, the anser D is incorrect. 15) Answer (C) is correct : Point of incedence. Explanation/Reason : The point of incidence is the point where the incident ray strikes the mirror. So, the missing label is C point of incident. ---------------

CHAPTER - 1 REFLECTION OF LIGHT AT CURVED SURFACES 37 SELF ASSESSMENT Very Short Answer Type Questions : [2 Marks] 1) What do you know about the terms given below related to spherical mirrors ? [2 M] a) Pole [2 M] b) Centre of curvature c) Focus. 2) How do you get a virtual image using a concave mirror ? 3) Where will the image be formed when we place an object on the principal axis of a concave mirror at a point between focus (F) and centre of curvature (C). [2 M] 4) Distinguish between real and virtual images.. [2 M] 5) Find the distance of the image when an object is placed on the principal axis at a distance of 10 cm in front of a concave mirror whose radius of curvature is 8 cm. [2 M] 6) State the laws of reflection. [2 M] 7) A ray of light is incident on a convex mirror as shown in the diagram . Redraw the diagram and complete the path of these rays after reflection from the mirror. Mark angle of incidence and angle of reflection on it. Also draw figure for concave mirror. [2 M] 8) How can we distinguish between a plane mirror, convex mirror and a concave mirror without touching them ? [2 M] 9) List out four specific characteristics of the images of the objects formed by convex mirrors. [2 M] 10) List two properties of the images formed by convex mirrors. Draw a ray diagram in support of your answer. . [2 M] 11) Write the characteristics of the image formed by a concave mirror when an object is placed. Between F and C. [2 M] 12) Rays from sun converge at a point 15 cm in front of a concave mirror. Where should an object be placed so that its image formed is equal to the size of the object ? [2M] 13) Under what condition in an arrangement of two plane mirrors, incident ray and reflected ray will always be parallel to each other, whatever may be the angle of incidence. [2 M] Show the same with the help of diagram. 1 4) List two possible ways in which a concave mirror can produce a magnified image of the object placed in front of it ? State the difference, if any, between these two images. [2M] 15) Identify the type of mirror used in the following : [ 2M] 1) Vehicle mirrors 2) Headlight of motor cycle 3) Spoon surface (back side) 4) Spoon surface (front side)