Light - Reflection and Refraction | PDF

ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 164 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction W e see a variety of objects in the world around us. However, we are unable to see anything in a dark room. On lighting up the matter, and light often behaves somewhat like a stream of particles. This confusion room, things become visible. What makes about the true nature of light continued for things visible? During the day, the sunlight some years till a modern quantum theory helps us to see objects. An object reﬂects light of light emerged in which light is neither a that falls on it. This reﬂected light, when ‘wave’ nor a ‘particle’ – the new theory received by our eyes, enables us to see things. reconciles the particle properties of light We are able to see through a transparent with the wave nature. medium as light is transmitted through it. There are a number of common wonderful phenomena associated with light such as image In this Chapter, we shall study the phenomena formation by mirrors, the twinkling of stars, the of reﬂection and refraction of light using the beautiful colours of a rainbow, bending of light straight-line propagation of light. These basic by a medium and so on. A study of the concepts will help us in the study of some of the properties of light helps us to explore them. optical phenomena in nature. We shall try to By observing the common optical understand in this Chapter the reﬂection of light phenomena around us, we may conclude that by spherical mirrors and refraction of light and light seems to travel in straight lines. The fact their application in real life situations. that a small source of light casts a sharp shadow of an opaque object points to this straight-line 9.1 REFLECTION OF LIGHT path of light, usually indicated as a ray of light. A highly polished surface, such as a mirror, reﬂects most of the light falling on it. You are already familiar with the laws of reﬂection of light. If an opaque object on the path of light becomes very small, light has a tendency Let us recall these laws – to bend around it and not walk in a straight (i) The angle of incidence is equal to the line – an eﬀect known as the diﬀraction of angle of reﬂection, and light. Then the straight-line treatment of (ii) The incident ray, the normal to the optics using rays fails. To explain mirror at the point of incidence and the phenomena such as diﬀraction, light is reﬂected ray, all lie in the same plane. thought of as a wave, the details of which These laws of reﬂection are applicable you will study in higher classes. Again, at to all types of reﬂecting surfaces including the beginning of the 20th century, it spherical surfaces. You are familiar with the became known that the wave theory of formation of image by a plane mirror. What are light often becomes inadequate for the properties of the image? Image formed by a treatment of the interaction of light with plane mirror is always virtual and erect. 166 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction The size of the image is equal to that of the of the sphere, is called a concave mirror. A object. The image formed is as far behind the spherical mirror whose reﬂecting surface is mirror as the object is in front of it. Further, the curved outwards, is called a convex mirror. The image is laterally inverted. How would the schematic representation of these mirrors is images be when the reﬂecting surfaces are shown in Fig. 9.1. You may note in these curved? Let us explore. diagrams that the back of the mirror is shaded. You may now understand that the surface of the spoon curved inwards can be approximated to a concave mirror and the Take a large shining spoon. Try to surface of the spoon bulged outwards can be view your face in its curved surface. approximated to a convex mirror. Do you get the image? Is it smaller or Before we move further on spherical larger? mirrors, we need to recognise and understand Move the spoon slowly away from your face. Observe the image. How the meaning of a few terms. These terms are does it change? commonly used in discussions about spherical Reverse the spoon and repeat the mirrors. The centre of the reﬂecting surface of a Activity. How does the image look spherical mirror is a point called the pole. It lies like now? on the surface of the mirror. The pole is usually Compare the characteristics of the represented by the letter P. image on the two surfaces. The curved surface of a shining spoon could be considered as a curved mirror. The most commonly used type of curved mirror is the spherical mirror. The reﬂecting surface of such mirrors can be considered to form a part of the surface of a sphere. Such mirrors, whose reﬂecting surfaces are spherical, are called spherical mirrors. We shall now study about spherical mirrors in some detail. 9.2 SPHERICAL MIRRORS The reﬂecting surface of a spherical mirror (a) Concave mirror (b) Convex mirror may be curved inwards or outwards. A spherical mirror, whose reﬂecting surface is Figure 9.1 Schematic representation of spherical mirrors; curved inwards, that is, faces towards the centre the shaded side is non-reﬂecting. 168 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction The reﬂecting surface of a spherical mirror The paper at ﬁrst begins to burn forms a part of a sphere. This sphere has a producing smoke. Eventually it may even catch centre. This point is called the centre of ﬁre. Why does it burn? The light from the Sun is curvature of the spherical mirror. It is converged at a point, as a sharp, bright spot represented by the letter C. Please note that the bythe mirror. In fact, this spot of light is the centre of curvature is not a part of the mirror. It image of the Sun on the sheet of paper. This lies outside its reﬂecting surface. The centre of point is the focus of the concave mirror. The curvature of a concave mirror lies in front of it. heat produced due to the concentration of However, it lies behind the mirror in case of a sunlight ignites the paper. The distance of this convex mirror. You may note this in Fig.9.2 (a) image from the position of the mirror gives the and (b). The radius of the sphere of which the approximate value of focal length of the mirror. reﬂecting surface of a spherical mirror forms a Let us try to understand this observation part, is called the radius of curvature of the with the help of a ray diagram. mirror. It is represented by the letter R. You may Observe Fig.9.2 (a) closely. A number of note that the distance PC is equal to the radius rays parallel to the principal axis are falling on a of curvature. Imagine a straight line passing concave mirror. Observe the reﬂected rays. through the pole and the centre of curvature of a They are all meeting/intersecting at a point on spherical mirror. This line is called the principal the principal axis of the mirror. This point is axis. Remember that principal axis is normal to called the principal focus of the concave mirror. the mirror at its pole. Let us understand an Similarly, observe Fig. 9.2 (b). How are the rays important term related to mirrors, through an parallel to the principal axis, reﬂected by a Activity. convex mirror? The reﬂected rays appear to come from a point on the principal axis. This point is called the principal focus of the convex mirror. The principal focus is represented by CAUTION: Do not look at the Sun the letter F. The distance between the pole and directly or even into a mirror reﬂecting the principal focus of a spherical mirror is sunlight. It may damage your eyes. called the focal length. It is represented by the Hold a concave mirror in your hand letter f. and direct its reﬂecting surface towards the Sun. Direct the light reﬂected by the mirror on to a sheet of paper held close to the mirror. (a) Move the sheet of paper back and forth gradually until you ﬁnd on the paper sheet a bright, sharp spot of light. Hold the mirror and the paper in the same position for a few minutes. What (b) do you observe? Why? Figure 9.2 (a) Concave mirror (b) Convex mirror 170 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction The reﬂecting surface of a spherical mirror Take a concave mirror. Find out its is by-and-large spherical. The surface, then, has approximate focal length in the way a circular outline. The diameter of the reﬂecting described above. Note down the value surface of spherical mirror is called its aperture. of focal length. (You can also ﬁnd it In Fig.9.2, distance MN represents the aperture. out by obtaining image of a distant We shall consider in our discussion only such object on a sheet of paper.) spherical mirrors whose aperture is much Mark a line on a Table with a chalk. smaller than its radius of curvature. Place the concave mirror on a stand. Is there a relationship between the radius Place the stand over the line such that of curvature R, and focal length f, of a spherical its pole lies over the line. mirror? For spherical mirrors of small Draw with a chalk two more lines apertures, the radius of curvature is found to be parallel to the previous line such that equal to twice the focal length. We put this as the distance between any two R = 2f. This implies that the principal focus of a successive lines is equal to the focal spherical mirror lies midway between the pole length of the mirror. These lines will and centre of curvature. now correspond to the positions of the points P, F and C, respectively. 9.2.1 Image Formation by Spherical Remember – For a spherical mirror of Mirrors small aperture, the principal focus F You have studied about the image lies mid-way between the pole P and formation by plane mirrors. You also know the the centre of curvature C. nature, position and relative size of the images Keep a bright object, say a burning formed by them. How about the images formed candle, at a position far beyond C. by spherical mirrors? How can we locate the Place a paper screen and move it in image formed by a concave mirror for diﬀerent front of the mirror till you obtain a positions of the object? Are the images real or sharp bright image of the candle ﬂame virtual? Are they enlarged, diminished or have on it. the same size? We shall explore this with an Observe the image carefully. Note Activity. down its nature, position and relative size with respect to the object size. Repeat the activity by placing the candle – (a) just beyond C, You have already learnt a way of (b) at C, (c) between F and C, (d) at F, determining the focal length of a concave and (e) between P and F. mirror. In Activity 9.2, you have seen that In one of the cases, you may not get the sharp bright spot of light you got on the image on the screen. Identify the the paper is, in fact, the image of the Sun. position of the object in such a case. It was a tiny, real, inverted image. You got Then, look for its virtual image in the the approximate focal length of the mirror itself. concave mirror by measuring the distance Note down and tabulate your of the image from the mirror. observations. 172 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction You will see in the above Activity that the object, an arbitrarily large number of rays nature, position and size of the image formed emanating from a point could be considered. by a concave mirror depends on the position of However, it is more convenient to consider the object in relation to points P, F and C. The only two rays, for the sake of clarity of the ray image formed is real for some positions of the diagram. These rays are so chosen that it is easy object. It is found to be a virtual image for a to know their directions after reﬂection from certain other position. The image is either the mirror. magniﬁed, reduced or has the same size, The intersection of at least two reﬂected depending on the position of the object. A rays give the position of image of the point summary of these observations is given for object. Any two of the following rays can be your reference in Table 9.1. considered for locating the image. Table 9.1 Image formation by a concave mirror for different positions of the object At inﬁnity At the focus F Highly diminished, Real and point-sized inverted Beyond C Between F and C Diminished Real and inverted (a) At C At C Same size Real and inverted Between C and F Beyond C Enlarged Real and inverted At F At inﬁnity Highly Real and enlarged inverted Between P and F Behind the Enlarged Virtual and mirror erect 9.2.2 Representation of Images Formed by Spherical Mirrors Using Ray Diagrams We can also study the formation of images (b) by spherical mirrors by drawing ray diagrams. Figure 9.3 Consider an extended object, of ﬁnite size, (i) A ray parallel to the principal axis, after placed in front of a spherical mirror. Each small reﬂection, will pass through the principal focus portion of the extended object acts like a point in case of a concave mirror or appear to diverge source. An inﬁnite number of rays originate fromthe principal focus in case of a convex from each of these points. To construct the ray mirror. This is illustrated in Fig.9.3 (a) and (b). diagrams, in order to locate the image of an 174 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction (ii) A ray passing through the principal focus of a concave mirror or a ray which is directed towards the principal focus of a convex mirror, after reﬂection, will emerge parallel to the principal axis. This is illustrated in Fig.9.4 (a) and (b). (b) Figure 9.5 (iv) A ray incident obliquely to the principal axis, towards a point P (pole of the mirror), on the concave mirror [Fig. 9.6 (a)] or a convex (a) mirror [Fig. 9.6 (b)], is reﬂected obliquely. The incident and reﬂected rays follow the laws of reﬂection at the point of incidence (point P), making equal angles with the principal axis. (b) (a) Figure 9.4 (iii) A ray passing through the centre of curvature of a concave mirror or directed in the direction of the centre of curvature of a convex mirror, after reﬂection, is reﬂected back along the same path. This is illustrated in Fig.9.5 (a) (b) and (b). The light rays come back along the Figure 9.6 same path because the incident rays fall on the mirror along the normal to the reﬂecting Remember that in all the above cases the surface. laws of reﬂection are followed. At the point of incidence, the incident ray is reﬂected in such a way that the angle of reﬂection equals the angle of incidence. (a) Image formation by Concave Mirror Figure 9.7 illustrates the ray diagrams for the formation of image by a concave mirror for (a) various positions of the object. 176 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Figure 9.7 Ray diagrams for the image formation by a concave mirror Uses of concave mirrors Concave mirrors are commonly used in Draw neat ray diagrams for each torches, search-lights and vehicles headlights position of the object shown in Table to get powerful parallel beams of light. They 9.1. are often used as shaving mirrors to see a larger You may take any two of the rays image of the face. The dentists use concave mentioned in the previous section for mirrors to see large images of the teeth of locating the image. patients. Large concave mirrors are used to Compare your diagram with those concentrate sunlight to produce heat in solar given in Fig. 9.7. Describe the nature, position and furnaces. relative size of the image formed in (b) Image formation by a Convex Mirror each case. Tabulate the results in a convenient We studied the image formation by a concave format. mirror. Now we shall study the formation of image by a convex mirror. 178 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Take a convex mirror. Hold it in one hand. Hold a pencil in the upright position in the other hand. Observe the image of the pencil in the mirror. Is the image erect or inverted? Is it diminished or enlarged? Figure 9.8 Formation of image by a convex mirror Move the pencil away from the mirror Table 9.2 Nature, position and relative size of slowly. Does the image become the image formed by a convex mirror smaller or larger? Repeat this Activity carefully. State whether the image will move closer to or farther away from the focus as the At inﬁnity At the focus F, Highly diminished, Virtual and object is moved away from the mirror? behind the mirror point-sized erect Between Between P and F, Diminished Virtual and inﬁnity behind the mirror erect and the pole P We consider two positions of the object for of the mirror studying the image formed by a convex mirror. First is when the object is at inﬁnity and the You have so far studied the image formation second position is when the object is at a ﬁnite by a plane mirror, a concave mirror and a distance from the mirror. The ray diagrams for convex mirror. Which of these mirrors will give the formation of image by a convex mirror for the full image of a large object? Let us explore these two positions of the object are shown in through an Activity. Fig.9.8 (a) and (b), respectively. The results are summarised in Table 9.2. Observe the image of a distant object, say a distant tree, in a plane mirror. Could you see a full-length image? Try with plane mirrors of different sizes. Did you see the entire object in the image? Repeat this Activity with a concave mirror. Did the mirror show full length image of the object? Now try using a convex mirror. Did you succeed? Explain your observations with reason. 180 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction You can see a full-length image of a tall 9.2.3 Sign Convention for Reﬂection by building/tree in a small convex mirror. One Spherical Mirrors such mirror is ﬁtted in a wall of Agra Fort facing Taj Mahal. If you visit the Agra Fort, try to While dealing with the reﬂection of light observe the full image of Taj Mahal. To view by spherical mirrors, we shall follow a set of distinctly, you should stand suitably at the sign conventions called the New Cartesian Sign terrace adjoining the wall. Convention. In this convention, the pole (P) of Uses of convex mirrors the mirror is taken as the origin (Fig. 9.9). The principal axis of the mirror is taken as the x-axis Convex mirrors are commonly used as (X’X) of the coordinate system. The rear-view (wing) mirrors in vehicles. These mirrors are ﬁtted on the sides of the vehicle, conventions are as follows – enabling the driver to see traﬃc behind him/her (i) The object is always placed to the left of to facilitate safe driving. Convex mirrors are the mirror. This implies that the light from preferred because they always give an erect, the object falls on the mirror from the left- though diminished, image. Also, they have a wider ﬁeld of view as they are curved outwards. hand side. Thus, convex mirrors enable the driver to view (ii) All distances parallel to the principal axis much larger area than would be possible with a are measured from the pole of the mirror. plane mirror. (iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along – x-axis) are taken as 1. Deﬁne the principal focus of a concave negative. mirror. (iv) Distances measured perpendicular to and 2. The radius of curvature of a spherical above the principal axis (along + y-axis) mirror is 20 cm. What is its focal are taken as positive. length? (v) Distances measured perpendicular to and 3. Name a mirror that can give an erect below the principal axis (along –y-axis) are taken as negative. and enlarged image of an object. The New Cartesian Sign Convention 4. Why do we prefer a convex mirror as a ? described above is illustrated in Fig.9.9 for rear-view mirror in vehicles? your reference. These sign conventions are applied to obtain the mirror formula and solve related numerical problems. 182 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction the object size. It is expressed as the ratio of the height of the image to the height of the object. It is usually represented by the letter m. I If h is the height of the object and h is the height of the image, then the magniﬁcation m produced by a spherical mirror is given by Height of the image (h ′ ) m= Height of the object (h ) h′ m= (9.2) Figure 9.9 h The New Cartesian Sign Convention for spherical mirrors The magniﬁcation m is also related to the object distance (u) and image distance (v). It can 9.2.4 Mirror Formula and Magniﬁcation be expressed as: In a spherical mirror, the distance of the h′ v Magniﬁcation (m) = = − (9.3) object from its pole is called the object distance h u (u). The distance of the image from the pole of the mirror is called the image distance (v). You You may note that the height of the object is already know that the distance of the principal taken to be positive as the object is usually focus from the pole is called the focal length (f). placed above the principal axis. The height of There is a relationship between these three the image should be taken as positive for virtual quantities given by the mirror formula which is images. However, it is to be taken as negative expressed as for real images. A negative sign in the value of the magniﬁcation indicates that the image is real. A positive sign in the value of the magniﬁcation 1 1 1 indicates that the image is virtual. + = (9.1) v u f Example 9.1 This formula is valid in all situations for all A convex mirror used for rear-view on an spherical mirrors for all positions of the object. automobile has a radius of curvature of 3.00 m. If You must use the New Cartesian Sign a bus is located at 5.00 m from this mirror, ﬁnd Convention while substituting numerical the position, nature and size of the image. values for u, v, f, and R in the mirror formula for Solution solving problems. Radius of curvature, R = + 3.00 m; Magniﬁcation Object-distance, u = – 5.00 m; Magniﬁcation produced by a spherical Image-distance, v = ? mirror gives the relative extent to which the Height of the image, hI = ? image of an object is magniﬁed with respect to 184 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 3.00 m 1 1 1 1 1 1 1 Focal length, f = R/2 = + = + 1.50 m (as or, v = f - u = - 15.0 - - 25.0 = - 15.0 + 25.0 2 the principal focus of a convex mirror is behind the mirror) 1 - 5.0 + 3.0 - 2.0 1 1 1 or, = = or, v = – 37.5 cm Since + = v 75.0 75.0 v u f The screen should be placed at 37.5 cm in front of the mirror. The image is real. 1 1 1 1 1 1 1 or, = - = + 1.50 – = + h' v v f u ( - 5.00) 1.50 5.00 Also, magniﬁcation, m = =- h u 5.00 +1.50 = vh (- 37.5cm) (+4.0 cm) 7.50 or, h ' = – = - (- 25.0 cm) u +7.50 v= 6.50 = + 1.15 m Height of the image, h ' = – 6.0 cm The image is 1.15 m at the back of the mirror. The image is inverted and enlarged. h' v 1.15 m Magniﬁcation, m = =- =– h u - 5.00 m = + 0.23 1. Find the focal length of a convex The image is virtual, erect and smaller in size by mirror whose radius of curvature is a factor of 0.23. 32 cm. Example 9.2 2. A concave mirror produces three An object, 4.0 cm in size, is placed at 25.0 cm in times magniﬁed (enlarged) real front of a concave mirror of focal length 15.0 image of an object placed at 10 cm in cm. At what distance from the mirror should a front of it. Where is the image screen be placed in order to obtain a sharp ? image? Find the nature and the size of the located? image. Solution Object-size, h = + 4.0 cm; 9.3 REFRACTION OF LIGHT Object-distance, u = – 25.0 cm; Focal length, f = –15.0 cm; Light seems to travel along straight-line Image-distance, v = ? paths in a transparent medium. What happens Image-size, h ' = ? when light enters from one transparent medium From Eq. (10.1): to another? Does it still move along a straight- 1 1 1 line path or change its direction? We shall recall + = some of our day-to-day experiences. v u f 186 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction You might have observed that the bottom of a tank or a pond containing water appears to Place a coin at the bottom of a bucket be raised. Similarly, when a thick glass slab is ﬁlled with water. placed over some printed matter, the letters With your eye to a side above water, try appear raised when viewed through the glass to pick up the coin in one go. Did you slab. Why does it happen? Have you seen a succeed in picking up the coin? Repeat the Activity. Why did you not pencil partly immersed in water in a glass succeed in doing it in one go? tumbler? It appears to be displaced at the Ask your friends to do this. Compare interface of air and water. You might have your experience with theirs. observed that a lemon kept in water in a glass tumbler appears to be bigger than its actual size, when viewed from the sides. How can you Place a large shallow bowl on a Table and put a coin in it. account for such experiences? Move away slowly from the bowl. Stop Let us consider the case of the apparent when the coin just disappears from your displacement of a pencil, partly immersed in sight. Ask a friend to pour water gently into water. The light reaching you from the portion the bowl without disturbing the coin. of the pencil inside water seems to come from a Keep looking for the coin from your different direction, compared to the part above position. Does the coin becomes visible water. This makes the pencil appear to be again from your position? How could this happen? displaced at the interface. For similar reasons, the letters appear to be raised, when seen The coin becomes visible again on through a glass slab placed over it. pouring water into the bowl. The coin appears slightly raised above its actual position due to Does a pencil appear to be displaced to the refraction of light. same extent, if instead of water, we use liquids like kerosene or turpentine? Will the letters appear to rise to the same height if we replace a Draw a thick straight line in ink, over a sheet of white paper placed on a Table. glass slab with a transparent plastic slab? You Place a glass slab over the line in such a will ﬁnd that the extent of the effect is different way that one of its edges makes an angle for different pair of media. These observations with the line. indicate that light does not travel in the same Look at the portion of the line under the slab from the sides. What do you direction in all media. It appears that when observe? Does the line under the glass travelling obliquely from one medium to slab appear to be bent at the edges? another, the direction of propagation of light in Next, place the glass slab such that it is the second medium changes. This phenomenon normal to the line. What do you observe now? Does the part of the line under the is known as refraction of light. Let us glass slab appear bent? understand this phenomenon further by doing a Look at the line from the top of the glass few activities. slab. Does the part of the line, beneath the slab, appear to be raised? Why does this happen? 188 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 9.3.1 Refraction through a Rectangular I the normal. At O , the light ray has entered from Glass Slab glass to air, that is, from a denser medium to a To understand the phenomenon of refraction of rarer medium. The light here has bent away light through a glass slab, let us do an Activity. from the normal. Compare the angle of incidence with the angle of refraction at both refracting surfaces AB and CD. Fix a sheet of white paper on a drawing In Fig. 9.10, a ray EO is obliquely incident board using drawing pins. on surface AB, called incident ray. OOI is the Place a rectangular glass slab over the refracted ray and OI H is the emergent ray. You sheet in the middle. Draw the outline of the slab with a may observe that the emergent ray is parallel to pencil. Let us name the outline as the direction of the incident ray. Why does it ABCD. happen so? The extent of bending of the ray of Take four identical pins. light at the opposite parallel faces AB (air-glass Fix two pins, say E and F, vertically interface) and CD (glass-air interface) of the such that the line joining the pins is rectangular glass slab is equal and opposite. inclined to the edge AB. This is why the ray emerges parallel to the Look for the images of the pins E and F incident ray. However, the light ray is shifted through the opposite edge. Fix two sideward slightly. What happens when a light other pins, say G and H, such that these ray is incident normally to the interface of two pins and the images of E and F lie on a media? Try and ﬁnd out. straight line. Remove the pins and the slab. Join the positions of tip of the pins E and F and produce the line up to AB. Let EF meet AB at O. Similarly, join the positions of tip of the pins G and H and produce it up to the edge CD. Let HG I meet CD at O. Join O and OI. Also produce EF up to P, as shown by a dotted line in Fig. 9.10. In this Activity, you will note, the light ray I has changed its direction at points O and O. Note that both the points O and OI lie on Figure 9.10 surfaces separating two transparent media. Refraction of light through a rectangular glass slab Draw a perpendicular NN’ to AB at O and another perpendicular MMI to CD at OI. The Now you are familiar with the refraction of light ray at point O has entered from a rarer light. Refraction is due to change in the speed of medium to a denser medium, that is, from air to light as it enters from one transparent medium glass. Note that the light ray has bent towards to another. Experiments show that refraction of light occurs according to certain laws. 190 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction The following are the laws of refraction of to that in vacuum. It reduces considerably in light. glass or water. The value of the refractive index for a given pair of media depends upon the (i) The incident ray, the refracted ray and the speed of light in the two media, as given below. normal to the interface of two transparent media at the point of incidence, all lie in the Consider a ray of light travelling from same plane. medium 1 into medium 2, as shown in Fig.9.11. Let v1 be the speed of light in medium 1 and v2 (ii) The ratio of sine of angle of incidence to the be the speed of light in medium 2. The sine of angle of refraction is a constant, for refractive index of medium 2 with respect to the light of a given colour and for the given medium 1 is given by the ratio of the speed of pair of media. This law is also known as light in medium 1 and the speed of light in Snell’s law of refraction. (This is true for medium 2. This is usually represented by the angle 0 < i < 90o) symbol n21. This can be expressed in an If i is the angle of incidence and r is the angle of equation form as refraction, then, Speed of light in medium 1 v1 sin i n21= = (9.5) = constant (9.4) Speed of light in medium 2 v 2 sin r This constant value is called the refractive index of the second medium with respect to the ﬁrst. Let us study about refractive index in some detail. 9.3.2 The Refractive Index You have already studied that a ray of light that travels obliquely from one transparent medium into another will change its direction in the second medium. The extent of the change Figure 9.11 in direction that takes place in a given pair of media may be expressed in terms of the refractive index, the “constant” appearing on By the same argument, the refractive index the right-hand side of Eq.(9.4). of medium 1 with respect to medium 2 is represented as n12. It is given by The refractive index can be linked to an Speed of light in medium 2 v 2 important physical quantity, the relative speed n12= = (9.6) Speed of light in medium 1 v1 of propagation of light in different media. It If medium 1 is vacuum or air, then the turns out that light propagates with different refractive index of medium 2 is considered with speeds in different media. Light travels fastest 8 –1 respect to vacuum. This is called the absolute in vacuum with speed of 3×10 m s. In air, the refractive index of the medium. It is simply speed of light is only marginally less, compared represented as n2. If c is the speed of light in air 192 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction and v is the speed of light in the medium, then, the refractive index of the medium nm is given by The ability of a medium to refract light is also expressed in terms of its optical density. Speed of light in air c Optical density has a deﬁnite connotation. It nm = = (9.7) Speed of light in the medium v is not the same as mass density. We have been using the terms ‘rarer medium’ and The absolute refractive index of a medium is ‘denser medium’ in this Chapter. It actually simply called its refractive index. The means ‘optically rarer medium’ and refractive index of several media is given in ‘optically denser medium’, respectively. Table 9.3. From the Table you can know that the When can we say that a medium is optically refractive index of water, nw = 1.33. This means denser than the other? In comparing two that the ratio of the speed of light in air and the media, the one with the larger refractive speed of light in water is equal to 1.33. index is optically denser medium than the Similarly, the refractive index of crown glass, other. The other medium of lower refractive ng =1.52. Such data are helpful in many places. index is optically rarer. The speed of light is However, you need not memorise the data. higher in a rarer medium than a denser medium. Thus, a ray of light travelling from Table 9.3 Absolute refractive index of some a rarer medium to a denser medium slows material media down and bends towards the normal. When it travels from a denser medium to a rarer Material medium, it speeds up and bends away from Refractive Material Refractive medium index medium index the normal. Air 1.0003 Canada 1.53 Balsam Ice 131 1. A ray of light travelling in air enters Water 1.33 Rock salt 1.54 Alcohol 1.36 obliquely into water. Does the light ray Kerosene 1.44 Carbon 1.63 bend towards the normal or away from disulphide Fused 1.46 the normal? Why? quartz Dense 1.65 2. Light enters from air to glass having ﬂint glass Turpentine 1.47 refractive index 1.50. What is the speed oil Ruby 1.71 of light in the glass? The speed of light in Benzene 1.50 Sapphire 1.77 vacuum is 3 × 108 m s–1. Crown 1.52 3. Find out, from Table 9.3, the medium glass Diamond 2.42 having highest optical density. Also ﬁnd the medium with lowest optical density. 4. You are given kerosene, turpentine and Note from Table 9.3 that an optically denser water. In which of these does the light medium may not possess greater mass density. travel fastest? Use the information given For example, kerosene having higher refractive ? in Table 9.3. index, is optically denser than water, although 5. The refractive index of diamond is 2.42. its mass density is less than water. What is the meaning of this statement? 194 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 9.3.3 Refraction by Spherical Lenses You might have seen watchmakers using a small magnifying glass to see tiny parts. Have you ever touched the surface of a magnifying glass with your hand? Is it plane surface or curved? Is it thicker in the middle or (b) at the edges? The glasses used in spectacles and that by a watchmaker are examples of lenses. Figure 9.12 What is a lens? How does it bend light rays? We (a) Converging action of a convex lens, shall discuss these in this section. (b) diverging action of a concave lens A transparent material bound by two surfaces, of which one or both surfaces are A lens, either a convex lens or a concave lens, spherical, forms a lens. This means that a lens is has two spherical surfaces. Each of these bound by at least one spherical surface. In such surfaces forms a part of a sphere. The centres of lenses, the other surface would be plane. A lens these spheres are called centres of curvature of may have two spherical surfaces, bulging the lens. The centre of curvature of a lens is outwards. Such a lens is called a double convex usually represented by the letter C. Since there lens. It is simply called a convex lens. It is are two centres of curvature, we may represent thicker at the middle as compared to the edges. them as C1 and C2. An imaginary straight line Convex lens converges light rays as shown in Fig. 9.12 (a). Hence convex lenses are also passing through the two centres of curvature of called converging lenses. Similarly, a double a lens is called its principal axis. The central concave lens is bounded by two spherical point of a lens is its optical centre. It is usually surfaces, curved inwards. It is thicker at the represented by the letter O. A ray of light edges than at the middle. Such lenses diverge through the optical centre of a lens passes light rays as shown in Fig. 9.12 (b). Such lenses without suﬀering any deviation. The eﬀective are also called diverging lenses. A double diameter of the circular outline of a spherical concave lens is simply called a concave lens. lens is called its aperture. We shall conﬁne our discussion in this Chapter to such lenses whose aperture is much less than its radius of curvature and the two centres of curvatures are equidistant from the optical centre O. Such lenses are called thin lenses with small apertures. What happens when parallel rays of light are incident on a lens? Let us do an Activity to understand this. (a) 196 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Observe Fig.9.12 (b) carefully. Several rays of light parallel to the principal axis are CAUTION: Do not look at the Sun directly falling on a concave lens. These rays, after or through a lens while doing this Activity refraction from the lens, are appearing to or otherwise. You may damage your eyes if diverge from a point on the principal axis. This you do so. point on the principal axis is called the principal Hold a convex lens in your hand. Direct focus of the concave lens. it towards the Sun. Focus the light from the Sun on a sheet If you pass parallel rays from the opposite of paper. Obtain a sharp bright image of surface of the lens, you get another principal focus on the opposite side. Letter F is usually the Sun. used to represent principal focus. However, a Hold the paper and the lens in the same lens has two principal foci. They are position for a while. Keep observing represented by F1 and F2. The distance of the the paper. What happened? Why? principal focus from the optical centre of a lens Recall your experience in Activity 9.2. is called its focal length. The letter f is used to represent the focal length. How can you ﬁnd the The paper begins to burn producing focal length of a convex lens? Recall the smoke. It may even catch ﬁre after a while. Activity 9.11. In this Activity, the distance Why does this happen? The light from the Sun between the position of the lens and the position constitutes parallel rays of light. These rays of the image of the Sun gives the approximate were converged by the lens at the sharp bright focal length of the lens. spot formed on the paper. In fact, the bright spot you got on the paper is a real image of the 9.3.4 Image Formation by Lenses Sun. The concentration of the sunlight at a point Lenses form images by refracting light. How do generated heat. This caused the paper to burn. lenses form images? What is their nature? Let us study this for a convex lens ﬁrst. Now, we shall consider rays of light parallel to the principal axis of a lens. What happens when you pass such rays of light through a lens? This is illustrated for a convex Ta k e a c o n v e x l e n s. F i n d i t s lens in Fig.9.12 (a) and for a concave lens in approximate focal length in a way Fig.9.12 (b). described in Activity 9.11. Draw ﬁve parallel straight lines, using Observe Fig.9.12 (a) carefully. Several chalk, on a long Table such that the rays of light parallel to the principal axis are distance between the successive lines is falling on a convex lens. These rays, after equal to the focal length of the lens. refraction from the lens, are converging to a Place the lens on a lens stand. Place it point on the principal axis. This point on the principal axis is called the principal focus of the on the central line such that the optical lens. Let us see now the action of a concave centre of the lens lies just over the line. lens. 198 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Let us now do an Activity to study the The two lines on either side of the lens nature, position and relative size of the image correspond to F and 2F of the lens formed by a concave lens. respectively. Mark them with appropriate letters such as 2F1, F1, F2 and 2F2, respectively. Take a concave lens. Place it on a Place a burning candle, far beyond 2F1 lens stand. to the left. Obtain a clear sharp image on Place a burning candle on one side of a screen on the opposite side of the lens. the lens. Note down the nature, position and Look through the lens from the other side and observe the image. Try to relative size of the image. get the image on a screen, if possible. Repeat this Activity by placing object If not, observe the image directly just behind 2F1, between F1 and 2F1 at through the lens. F1, between F1 and O. Note down and Note down the nature, relative size tabulate your observations. and approximate position of the image. Move the candle away from the lens. The nature, position and relative size of the Note the change in the size of the image. What happens to the size of image formed by convex lens for various the image when the candle is placed positions of the object is summarised in Table too far away from the lens. 9.4. Table 9.4 Nature, position and relative size of The summary of the above Activity is given in the image formed by a convex lens for various Table 9.5 below. positions of the object Table 9.5 Nature, position and relative size of the image formed by a concave lens for various positions of the object At inﬁnity At the focus F2 Highly diminished, Real and inverted point-sized Beyond 2F Between F2 and 2F2 Diminished Real and inverted At inﬁnity At focus F1 Highly diminished, Virtual At 2F1 At 2F2 Same size Real and inverted point-sized and erect Between F1 and 2F1 Beyond 2F2 Enlarged Real and inverted At Focus F1 At inﬁnity Inﬁnitely large or Real and inverted Between inﬁnity Between focus F1 Diminished Virtual and erect Highly enlarged and and optical centre O Between P and Behind the mirror Enlarged Virtual and erect optical centre O and optical of the lens of the lens centre O as the object 200 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction What conclusion can you draw from this (ii) A ray of light passing through a principal Activity? A concave lens will always give a focus, after refraction from a convex lens, virtual, erect and diminished image, will emerge parallel to the principal axis. irrespective of the position of the object. This is shown in Fig. 9.14 (a). A ray of light appearing to meet at the principal 9.3.5 Image Formation in Lenses Using Ray focus of a concave lens, after refraction, Diagrams will emerge parallel to the principal axis. We can represent image formation by lenses This is shown in Fig.9.14 (b). using ray diagrams. Ray diagrams will also help us to study the nature, position and relative size of the image formed by lenses. For drawing (a) ray diagrams in lenses, alike of spherical mirrors, we consider any two of the following rays – (i) A ray of light from the object, parallel to (b) the principal axis, after refraction from a convex lens, passes through the principal focus on the other side of the lens, as Figure 9.14 shown in Fig. 9.13 (a). In case of a concave lens, the ray appears to diverge (iii) A ray of light passing through the optical from the principal focus located on the centre of a lens will emerge without any same side of the lens, as shown in Fig. deviation. This is illustrated in Fig.9.15(a) 9.13 (b). and Fig.9.15 (b). (a) (a) (b) Figure 9.15 The ray diagrams for the image formation in a convex lens for a few positions of the object are shown in Fig. 9.16. The ray diagrams (b) representing the image formation in a concave Figure 9.13 lens for various positions of the object are shown in Fig. 9.17. 202 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Figure 9.16 The position, size and the nature of the image formed by a convex lens for various positions of the object Figure 9.17 Nature, position and relative size of the image formed by a concave lens 204 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 9.3.6 Sign Convention for Spherical Lenses Magniﬁcation produced by a lens is also related to the object-distance u, and the image- For lenses, we follow sign convention, similar distance v. This relationship is given by to the one used for spherical mirrors. We apply the rules for signs of distances, except that all I Magniﬁcation (m) = h / h = v/u (9.10) measurements are taken from the optical centre of the lens. According to the convention, the Example 9.3 focal length of a convex lens is positive and that of a concave lens is negative. You must take A concave lens has focal length of 15 cm. At care to apply appropriate signs for the values of what distance should the object from the lens be I u, v, f, object height h and image height h. placed so that it forms an image at 10 cm from the lens? Also, ﬁnd the magniﬁcation produced by the lens. 9.3.7 Lens Formula and Magniﬁcation Solution As we have a formula for spherical mirrors, we also have formula for spherical lenses. This A concave lens always forms a virtual, erect formula gives the relationship between object- image on the same side of the object. distance (u), image-distance (v) and the focal Image-distance v = –10 cm; length (f). The lens formula is expressed as Focal length f = –15 cm; Object-distance u = ? 1 1 1 − = (9.8) v u f 1 1 1 Since - = The lens formula given above is general v u f and is valid in all situations for any spherical or, 1 - 1 = 1 lens. Take proper care of the signs of different u v f quantities, while putting numerical values for solving problems relating to lenses. 1 1 1 1 1 = - =- + u -10 (-15) 10 15 Magniﬁcation 1 1 The magniﬁcation produced by a lens, similar = -3+2 = u 30 -30 to that for spherical mirrors, is deﬁned as the or, u = – 30 cm ratio of the height of the image and the height of Thus, the object-distance is 30 cm. the object. Magniﬁcation is represented by the Magniﬁcation m = v/u letter m. If h is the height of the object and hI is the height of the image given by a lens, then the m = -10cm = 1 @ + 0.33 magniﬁcation produced by the lens is given by, -30cm 3 The positive sign shows that the image is erect Height of the Image h ′ m= = (9.9) and virtual. The image is one-third of the size of Height of the object h the object. 206 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Example 9.4 The negative signs of m and h I show that the A 2.0 cm tall object is placed perpendicular to image is inverted and real. It is formed below the principal axis of a convex lens of focal the principal axis. Thus, a real, inverted image, 4 cm tall, is formed at a distance of 30 cm on the length 10 cm. The distance of the object from other side of the lens. The image is two times the lens is 15 cm. Find the nature, position and enlarged. size of the image. Also ﬁnd its magniﬁcation. Solution 9.3.8 Power of a Lens Height of the object h = + 2.0 cm; You have already learnt that the ability of a lens Focal length f = + 10 cm; to converge or diverge light rays depends on its object-distance u = –15 cm; focal length. For example, a convex lens of Image-distance v = ? short focal length bends the light rays through Height of the image hI = ? large angles, by focussing them closer to the optical centre. Similarly, concave lens of very 1 1 1 short focal length causes higher divergence Since - = than the one with longer focal length. The v u f degree of convergence or divergence of light rays achieved by a lens is expressed in terms of 1 1 1 or, = + its power. The power of a lens is deﬁned as the v u f reciprocal of its focal length. It is represented 1 1 1 1 1 by the letter P. The power P of a lens of focal = + =- + v (-15) 10 15 10 length f is given by 1 1 = -2+3 = 1 v 30 30 P= (9.11) f or, v = +30 cm The SI unit of power of a lens is ‘dioptre’. The positive sign of v shows that the image is It is denoted by the letter D. If f is expressed in formed at a distance of 30 cm on the other side metres, then, power is expressed in dioptres. of the optical centre. The image is real and Thus, 1 dioptre is the power of a lens whose inverted. –1 focal length is 1 metre. 1D = 1m. You may note hI v that the power of a convex lens is positive and Magniﬁcation m = = h u that of a concave lens is negative. I Opticians prescribe corrective lenses or, h = h (v / u) indicating their powers. Let us say the lens Height of the image, hI= (2.0) (+30/–15) = – 4.0 cm prescribed has power equal to + 2.0 D. This means the lens prescribed is convex. The focal Magniﬁcation m = v/u length of the lens is + 0.50 m. Similarly, a lens +30 cm = -2 of power – 2.5 D has a focal length of – 0.40 m. or, m= The lens is concave. -15 cm 208 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction The simple additive property of the powers of lenses can be used to design Many optical instruments consist of a lens systems to minimise certain defects number of lenses. They are combined to in images produced by a single lens. Such increase the magniﬁcation and sharpness a lens system, consisting of several lenses, of the image. The net power (P) of the in contact, is commonly used in the design lenses placed in contact is given by the of lenses of camera, microscopes and algebraic sum of the individual powers P1, telescopes. P2, P3, … as P = P1 + P2 + P3 + … The use of powers, instead of focal lengths, for lenses is quite convenient for opticians. During eye-testing, an optician puts several different combinations of 1. Deﬁne 1 dioptre of power of a lens. 2. A convex lens forms a real and inverted corrective lenses of known power, in image of a needle at a distance of 50 cm contact, inside the testing spectacles’ from it. Where is the needle placed in frame. The optician calculates the power of the lens required by simple algebraic front of the convex lens if the image is addition. For example, a combination of equal to the size of the object? Also, ﬁnd ? two lenses of power + 2.0 D and + 0.25 D the power of the lens. 3. Find the power of a concave lens of focal is equivalent to a single lens of power length 2 m. + 2.25 D. Light seems to travel in straight lines. Mirrors and lenses form images of objects. Images can be either real or virtual, depending on the position of the object. The reﬂecting surfaces, of all types, obey the laws of reﬂection. The refracting surfaces obey the laws of refraction. New Cartesian Sign Conventions are followed for spherical mirrors and lenses. 1 1 1 Mirror formula, + = , gives the relationship between the object-distance (u), v u f image-distance (v), and focal length (f) of a spherical mirror. The focal length of a spherical mirror is equal to half its radius of curvature. The magniﬁcation produced by a spherical mirror is the ratio of the height of the image to the height of the object. A light ray travelling obliquely from a denser medium to a rarer medium bends away from the normal. A light ray bends towards the normal when it travels obliquely from a rarer to a denser medium. 210 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction Light travels in vacuum with an enormous speed of 3×108 m s-1. The speed of light is different in different media. The refractive index of a transparent medium is the ratio of the speed of light in vacuum to that in the medium. In case of a rectangular glass slab, the refraction takes place at both air-glass interface and glass-air interface. The emergent ray is parallel to the direction of incident ray. Lens formula, 1 - 1 = 1 , gives the relationship between the object-distance (u), v u f image-distance (v), and the focal length (f) of a spherical lens. Power of a lens is the reciprocal of its focal length. The SI unit of power of a lens is dioptre. 1. Which one of the following materials cannot be used to make a lens? (a) Water (b) Glass (c) Plastic (d) Clay 2. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Where should be the position of the object? (a) Between the principal focus and the centre of curvature (b) At the centre of curvature (c) Beyond the centre of curvature (d) Between the pole of the mirror and its principal focus. 3. Where should an object be placed in front of a convex lens to get a real image of the size of the object? (a) At the principal focus of the lens (b) At twice the focal length (c) At inﬁnity (d) Between the optical centre of the lens and its principal focus. 4. A spherical mirror and a thin spherical lens have each a focal length of –15 cm. The mirror and the lens are likely to be (a) both concave. (b) both convex. (c) the mirror is concave and the lens is convex. (d) the mirror is convex, but the lens is concave. 5. No matter how far you stand from a mirror, your image appears erect. The mirror is likely to be (a) only plane. (b) only concave. (c) only convex. (d) either plane or convex. 212 ANDHRA PRADESH | PHYSICAL SCIENCE : Light – Reflection and Refraction 6. Which of the following lenses would you prefer to use while reading small letters found in a dictionary? (a) A convex lens of focal length 50 cm. (b) A concave lens of focal length 50 cm. (c) A convex lens of focal length 5 cm. (d) A concave lens of focal length 5 cm. 7. We wish to obtain an erect image of an object, using a concave mirror of focal length 15 cm. What should be the range of distance of the object from the mirror? What is the nature of the image? Is the image larger or smaller than the object? Draw a ray diagram to show the image formation in this case. 8. Name the type of mirror used in the following situations. (a) Headlights of a car. (b) Side/rear-view mirror of a vehicle. (c) Solar furnace. Support your answer with reason. 9. One-half of a convex lens is covered with a black paper. Will this lens produce a complete image of the object? Verify your answer experimentally. Explain your observations. 10. An object 5 cm in length is held 25 cm away from a converging lens of focal length 10 cm. Draw the ray diagram and ﬁnd the position, size and the nature of the image formed. 11. A concave lens of focal length 15 cm forms an image 10 cm from the lens. How far is the object placed from the lens? Draw the ray diagram. 12. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find the position and nature of the image. 13. The magniﬁcation produced by a plane mirror is +1. What does this mean? 14. An object 5.0 cm in length is placed at a distance of 20 cm in front of a convex mirror of radius of curvature 30 cm. Find the position of the image, its nature and size. 15. An object of size 7.0 cm is placed at 27 cm in front of a concave mirror of focal length 18 cm. At what distance from the mirror should a screen be placed, so that a sharp focussed image can be obtained? Find the size and the nature of the image. 16. Find the focal length of a lens of power – 2.0 D. What type of lens is this? 17. A doctor has prescribed a corrective lens of power +1.5 D. Find the focal length of the lens. Is the prescribed lens diverging or converging? 214

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