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1 REFRACTION OF LIGHT GUPTA CLASSES For any help contact: , Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: ,

2 Reraction o light:. The ratio o the sine o the angle o incidence to the sine o the angle o reraction is a constant whose value depends on sin i v the nature o the two mediums. This is called as Snell s law. According to this law, sin r v where is called the reractive index o medium with respect to medium.. I the medium is vacuum, then v = c and the index o reraction o the medium w.r.t. the vacuum is: = c/v. It is also called absolute reractive index o medium. 3. Because the speed o light is dierent in dierent mediums and requency remains unchanged on passing rom one air medium to other, hence wavelength o light gets changed with change in medium. The relation is: medium. Thus, when a light ray rom a rarer medium is reracted into a denser medium, its velocity decreases and wavelength decreases but the requency does not change. 4. For air =.0003 which may be taken as. Thereore, when light passes rom air into any transparent solid the reractive index is always >. 5. The value o reractive index depends on nature o medium and wavelength or colour o light. 6. Reractive index is independent o the angle o incidence. 7. Reractive index decreases with increase in temperature. 8. When the medium is same on both sides o a glass slab, then the deviation o the emergent ray is zero. That is the t sin (i r) emergent ray goes parallel to the incident ray and lateral displacement o the emergent ray y = (where t = cos r thickness o slab). 9. Cauchy's ormula : The reractive index o a material depends on the wavelength o light according to the B relation: A (where A and B are constants) 0. I a n g and a n w, are the reractive indices o glass and water w.r.t. air respectively, then reractive index o glass w.r.t. water is: w n Real and apparent depth: g a a n n g w REFRACTION OF LIGHT. I a beaker is illed with water and a person in air observes an object lying at its bottom, then the object appears raised. actual depth (dac ) The apparent depth d ap is less than the actual depth t ac can be shown that apparent depth (dap ) reractive index( ) d. I there is an ink spot at the bottom o a glass slab, it appears to be raised by a distance y dac dap d d where d is the thickness o the glass slab and is its reractive index. 3. I a beaker is illed with immissible transparent liquids o reractive indices,, 3 and individual depth d, d, d 3 d d d 3 respectively, then the apparent depth o the beaker is ound to be: d ap 3 Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: ,

3 Total internal relection:. For the phenomenon o total internal relection to take place, it is necessary that a light ray must travel rom a denser medium to a rarer medium, and the angle o incidence in the denser medium must be greater the critical angle or the given two media.. The critical angle is that angle o incidence or which the angle o reraction becomes 90. It is given by: sin ic I the rarer medium is air or vacuum, then sin i R c 3. Critical angle or red light is more than that or blue light. 4. Critical angle increases with the increase in temperature o the medium. D 5. Critical angle depends on (i) nature o medium, (ii) temperature o medium and (iii) wavelength o light. 6. Air bubbles in glass appear silvery white due to total internal relection. 7. A diver in water at a depth d sees the world outside through a horizontal circle o radius r d tan i d / 8. The brilliance o diamond is due to the phenomenon o total internal relection. 9. Mirages in deserts are also due to reraction and total internal relection. 0. The working o optical ibre is based on the phenomenon o total internal relection. Optical iber:. It is a glass iber through which light is transmitted by total internal relections rom one end to other end. An optical iber may be between 0.0 mm and 0.00 mm in diameter and may be used in bundles with the same relative positions at both the ends. It is also called as light pipe. 3. For working o the optical iber, the angle o incidence should be according to relation reractive index o the material used or cladding o the pipe and is the reractive index o the core o the pipe. sini c, where is the 4. Optical ibers are used in the ield o communications and computers or transmitting and receiving signals converted into light pulses. They also have medical uses such as in Endoscopy. Spherical reracting surace:. A spherical reracting surace is a portion o a reracting medium whose curved surace is a part o a sphere. Convex and concave spherical reracting suraces are shown in Fig.. The pole, centre o curvature, radius o curvature, aperture, the principal axis, etc., are deined in the same manner as or mirrors. 3. Suppose an object is placed in a medium o reractive index. The spherical curved surace (convex or concave) separates it rom another medium o reractive index Then, i u, v and R are respectively the object distance, the image distance and the radius o curvature o the reracting surace, then the ormula or relating u, v and R is: v u R 4. I the object is placed in the medium o reractive index and the curved surace separates it rom medium then the ormula is v u R Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: ,

4 Lenses:. A lens is a piece o transparent reractive medium (such as glass, plastic or liquid) bounded by two suraces one o which at least must be spherical.. When a lens is thicker in the middle than at the edges, it is called a convex lens or converging lens. When the lens is thicker at the edges than in the middle, it is called as concave lens or diverging lens. 3. A thin lens is one in which the distance between the two suraces along the principal axis is negligibly small. In case o a thin lens, distances measured rom the poles o the reracting suraces can be taken as the distances measured rom the optical centre o the lens. Optical centre is a point through which a light ray passes undeviated i the lens is quite thin, Lens Maker's ormula and thin lens ormula:. When medium is same on both sides o a lens, then ( ) where = ocal length o the thin v u R R lens, = reractive index o the material o lens with respect to the medium surrounding it, R = radius o curvature o the irst surace and R = radius o curvature o the second surace.. For a plano-convex lens or plano-concave lens, is negative or a plano-concave lens. 3. I radii o curvatures o the two suraces are the same, say R, then Power & magniication due to a lens: Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: , ( ) The ocal length is positive or a plano-convex lens, while it R R. ( ). Linear magniication is the ratio o the size o image (I) to the size o the object (O), i.e., m = I/O. v v. For a thin lens (convex or concave) m or m or m u u 3. For a real image m is negative and or a virtual image m is positive. 4. The power o a lens P =(/) dioptre (D). where is ocal length in metre. Combination o Lenses:. Whenever two lenses are in contact, the reciprocal o eective ocal length is equal to the sum o the reciprocals o ocal lengths o the lenses in contact.. The power o the combination o two lenses in contact is equal to the sum o the powers o the individual lenses, i.e., P = P + P. 3. I two thin lenses are separated by a small distance d, then the ocal length o the combination is: Some more points about lenses: d g. When a lens is kept in a medium other than air, then where m is the reractive index o the m m R R medium in which lens is placed.. When a lens is placed in a medium or which is less than that o the lens, its ocal length increases and power decreases- The nature o the lens remains unchanged. 3. When the lens is placed in a medium or which is equal to that o the lens, the ocal length o the lens becomes ininity and power becomes zero. The lens behaves like a plane glass plate. 4

5 4. When the lens is placed in a medium or which is greater than that o the lens, the nature o the lens changes. (Air bubble in water behaves as a divergent lens.) 5. When a lens o ocal length is cut into two equal halves perpendicular to principal axis, then each part o the lens has a ocal length. 6. When a lens o ocal length is cut into two equal halves parallel to principal axis, then each part has a ocal length. The intensity o image is decreased. 7. For a real image the distance (d) between convex lens and screen must be greater or equal to 4. When d < 4 then there is no real image on screen. When d = 4 then there is only one positions o the lens or which image o the object on the screen is distinct and clear When d > 4 then there are two positions o the lens or which the image o the object on the screen is distinct and clear. In these two positions o lens, the distances o object and image rom the lens are interchanged. In this case i size o image in one position is I and in other I then size o object (O) is given by O I I REFRACTION OF LIGHT Assignment. The reractive index o water with respect to air is 4/3 and the reractive index o glass with respect to air is 3/. Then the reractive index o water with respect to glass is; (a) 9/8 (b) 8/9 (c) / (d). I μ ij represents the reractive index when a light ray goes rom medium i to medium j then the product μ x μ 3 x μ 43 is equal to: (a) μ 3 (b) μ 4 (c) μ 3 (d) /μ 4 3. The reractive index o a given piece o transparent quartz is greatest or: (a) red light (b) violet light (c) green light (d) yellow light 4. A plane glass slab is kept over various coloured letters; the letter which appears least raised is: (a) blue (b) violet (c) green (d) red 5. A glass slab ( =.5) o thickness 3.0 cm is placed on an ink spot. A person looks at it rom a distance o 5.0 cm above the ink spot. The distance o the spot will appear to be: (a).0 cm (b) 3.5 cm (c) 4.0 cm (d) 5.0 cm 6. The length o a vertical pole at the surace o a lake o water ( = 4/3) is 4 cm. Then to an underwater ish just below the water surace the tip o the pole appears to be: (a) 8 cm above the surace (b) 4 cm above the surace (c) 3 cm above the surace (d) 36 cm above the surace 7. An air bubble in a glass slab (μ =.5) is 5 cm deep when viewed rom, one ace and cm deep, when viewed rom the opposite ace. The thickness o the slab is; (a) 7.5 cm (b) 0.5 cm (c) 7 cm (d) 0 cm Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: , A bird in air looks at a ish vertically below it and inside water; h is the height o the bird above the surace o water and h the depth o the ish below the surace o water. I reractive index o water with respect to air be μ then the distance o the ish as observed by the bird is: (a) h + h (b) h + h / μ (c) μ h + h (d) μ (h + h ) 9. Critical angle o light passing rom glass to air is minimum or: (a) red (b) green (c) yellow (d) violet 0. The reractive index o water is 4/3 and that o glass is 5/3. Then the critical angle or a ray o light entering water rom glass will be: (a) sin - (4/5) (b) sin - (5/4) (c) sin - (0/9) (d) sin - (9/0). A diver in a swimming pool wants to signal his distress to a person lying on the edge o the pool by lashing his waterproo lash light: (a) he must direct the beam vertically upwards (b) he has to direct the beam horizontally (c) he has to direct the beam at an angle to the vertical which is slightly less than the critical angle o incidence or total internal relection (d) he has to direct the beam at an angle to the vertical which is slightly more than the critical angle o incidence or total internal relection. The critical angle or light going rom medium x into medium y is θ. The speed o light in medium x is v. The speed o light in medium y is: (a) v(l - cos θ) (b) v/sin θ (c) v/cos θ (d) v cos θ 3. A point source o light is placed 4 m below the surace o water o reractive index 5/3. The 5

6 minimum diameter o a disc, which should be placed over the source, on the surace o water to cut o all light coming out o water is: (a) m (b) 4 m (c) 3 m (d) 6 m 4. A thin convergent glass lens ( g =.5) has a power o When this lens is immersed in a liquid o reractive index l it acts as a divergent lens o ocal length 00 cm. The value o l is (a) 4/3 (b) 5/3 (c) 5/4 (d) 6/5 5. A double convex lens o ocal length 6 cm is made o glass o reractive index.5. The radius o curvature o one surace is double that o the other surace. The value o smaller radius o curvature is: (a) 6 cm (b) 4.5 cm (c) 9 cm (d) 4 cm 6. To obtain magniied virtual image o an object by a convex lens o ocal length, the distance between the object and the lens should be: (a) > 4 (b) between and 4 (c) < (d) >6 7. A thin lens has ocal length and its aperture has diameter d. It orms an image o intensity I, Now, the central part o the aperture up to diameter (d/) is blocked by an opaque paper. The ocal length and image intensity will change to: (b) (/) and (I/) (b) and (I/4) (c) (3/4) and (I/) (d) and (3I/4) 8. Diameter o a plano-convex lens is 6 cm and thickness at the centre is 3 mm. I the speed o light in the material o the lens is x 0 8 m/s, the ocal length o the lens is: (a) 5 cm (b) 0 cm (c) 30cm (d) 0cm 9. A magniying glass is to be used at the ixed object distance o cm. I it is to produce an erect image magniied 5 times, its ocal length is (a).5 cm (b) -.5 cm (c) 5.0cm (d) none o these 0. Two thin lenses are in contact and the ocal length o the combination is 80 cm. I the ocal length o one o the lenses is 0 cm, the power o the other lens is: (a).66 (b) 4.00 (c) -.00 (d) A convex lens o power + 6 is placed in contact with a concave tens o power 4. What is the nature and ocal length o the combination? (a) Concave, 5 cm (b) Convex, 50 cm (c) Concave, 0 cm (d) Convex, 00 cm. An equiconvex glass lens (a) has a ocal length and power P. It is cut into two symmetrical halves (b) by a plane containing the principal axis. The two pieces are recombined as shown in Fig (c). The power o new combina tion is: (a) P (b) P/ (c) P (d) zero 3. Two thin convex lenses o ocal lengths 0 cm and 5 cm, respectively, are placed at a distance d. I a parallel beam incident on the irst lens emerges as a parallel beam rom the second lens, then the value o d is: (a) 5 cm (b) 5 cm (c) 0cm (d) 5cm 4. Focal length o a lens or red colour is: (a) same as that or violet (b) greater than that or violet (c) lesser than that o violet (d) none o the above 5. A thin convex lens o crown glass ( =.5) has a power o. Another convex lens with the same radii o curvature and made up o a glass material with reractive index.6 will have a power o: (a). (b) -0.9 (c) -0.8 (d) A lamp is placed 6.0 m rom a wall. On putting a lens between the lamp and the wall at a distance o. m rom the lamp, a real image o the lamp is ormed on the wall. The magniication o the image is: (a) 3 (b) 4 (c) 5 (d) 6 7. A plano-convex lens o ocal length 0 cm silvered at the plane surace will behave as convergent mirror o ocal length: (a) 0 cm (b) 30 cm (c) 40cm (d) 0cm 8. A real image is ormed by a convex lens. I we put it in contact with a concave lens and the combination again orms a real image, which o the ollowing is true or the new image rom the combination? (a) Shits towards the lens system (b) Shits away rom the lens system (c) Remains at the original position (d) No image is ormed 9. A concave lens o ocal length 0 cm placed in contact with a plane mirror acts as a: (a) convex mirror o ocal length 0 cm (b) concave mirror o ocal length 40 cm (c) concave mirror o ocal length 60 cm (d) concave mirror o ocal length 0 cm Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: ,

7 30. A symmetrical double convex lens is cut in two equal parts by a plane containing the principal axis. I the power o the original lens was 4, the power o a divided lens will be: (a) (b) 3 (c) 4 (d) 5 3. A convex lens o ocal length 0 cm is cut into two equal parts so as to obtain two plano-convex lenses as shown in igure, The two parts are then put in contact as shown in igure. What is the ocal length o the combination? (a) Zero (b) 5 cm (c) 0 cm (d) 0 cm 3. In the igure given below there are two convex lenses L and L having ocal lengths F and F respectively. The distance between L and L will be: (a) F (b) F (c) F + F (d) F F 33. B and R are the ocal lengths o a convex lens or blue and red light respectively and F B and F R are the ocal lengths o a concave lens or blue and red light respectively. We must then have: (a) B < R and F B < F R (b) B < R and F B > F R (b) B > R and F B > F R (d) B > R and F B < F R ANSWERS b,d,3b,4d,5c,6c,7b,8b,9d,0a,c,b,3d,4b,5b,6c,7d,8c,9a,0d,b,d,3d,4b,5a,6b,7d,8b,9a,30c,3d,3c,33a Nishant Gupta, D-, Prashant vihar, Rohini, Delhi-85 Contact: ,

always positive for virtual image

always positive for virtual image Point to be remembered: sign convention for Spherical mirror Object height, h = always positive Always +ve for virtual image Image height h = Always ve for real image. Object distance from pole (u) = always