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Refraction at plane surface and Prisms Dr. M K Raghavendra BASE, Bangalore

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Type 1 – Snell’s law and RI Snell’s law: Relative R I in terms of speed of light Relative R I in terms of absolute R I Absolute R I in terms of speed of light Modified Snell’s law Relative R I in terms of wavelength of light Frequency remains constant

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1)A ray of light is incident on the interface of two media at an angle of 45 0 and is refracted in to the other medium at an angle of 30 0. If the speed of light in the first medium is 3X10 8 ms -1,what is the speed of light in the second medium? (1)1.96X10 8 ms -1 (2)2.12X10 8 ms -1 (3)3.18X10 8 ms -1 (4) 3.33X10 8 ms -1

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Snell’s law: Thus

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2)A ray of light is travelling from medium A to medium B. The angle of incidence is i and that of refraction is r. Graph between sin(i) and sin(r) is as shown in Figure below. We can conclude the following (i) Speed of light in medium B is three-fourth of that in medium A. (ii) Total internal reflection cannot take place. (iii) Refractive index of medium B is greater than that of medium A. Correct conclusions are (1)Only (i) and (ii) (2) Only (ii) and (iii) (3) (i), (ii) and (iii) (4) Only (i) and (iii) sin (r) sin (i) O 37 0

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The slope of the straight line: Medium B is denser than medium A Since n b > n a TIR cannot take place sin (r) sin (i) O 37 0 sin (i) sin (r)

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3) Given refractive index of glass with respect to air is a n g = 3/2 and that of water with respect to air is a n w = 4/3, the refractive index of glass with respect to water is (1)8/9 (2) 9/8 (3)2 (4)1/2

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Type 2: Normal Shift and Lateral Shift Lateral shift Normal shift a) Object in denser b) Object in rarer

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4) A vessel of height h is filled with a liquid of refractive index n 1 to a height h/2 and the upper half of the vessel is filled with a liquid of refractive index n 2. The apparent depth of the vessel as seen along the normal is 1) 2) 3) 4)

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In case of one liquid the apparent depth is given by In case of many layers of liquid

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5) A ray of light passes through four transparent media with refractive indices 1 2 3 and 4 as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have (1) 1 = 2 (2) 2 = 3 (3) 3 = 4 (4) 4 = 1 A B C D

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Apply to medium 1 and medium 4 Since ray AB and CD are parallel, i 1 and i 4 are equal Implies 1 = 4

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6) An ink dot on a paper placed on a table top is viewed from a distance of 30 cm above it with the help of a telescope. A 16 cm thick glass slab is placed on the ink dot. By what distance the telescope should be raised to refocus the ink dot ? The refractive index of glass is 1.6. (1)3 cm (2)4 cm (3)5 cm (4)6 cm

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The telescope should be moved up by a distance (y) equal to normal shift produced by the slab

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7) Consider the situation shown in the figure. The bottom of the vessel is a plane mirror, S is a small fish located at a height of H/2 from the plane of the mirror, T is a human eye located at a height of H from the surface of water. The distances at which the fish sees the images of the eye (with respect to its position) are 1) 2) 3) 4) S T H ( H/2) H

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S T H H Image 1 nH + H/2 Image 2 nH + H nH + H+H/2 Image 1: H (n+1/2) Image 2: H (n+3/2) A.P = nH

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Type 3: Critical angle and Total Internal Reflection

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8) A, B and C are three optical media of respective critical angles C 1, C 2 and C 3. Total internal reflection of light can occur from A to B and also from B to C but not from C to A. Then the correct relation between critical angles is (1)C 1 >C 2 >C 3 (2) C 1 = C 2 = C 3 (3)C 3 > C 1 > C 2 (4)C 1 <C 2 <C 3

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T I R can occur when light travels from medium A to medium B T I R can occur when light travels from medium B to medium C Therefore

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9) What is the critical angle, C for calcite ( =1.5) immersed in oil ( =1.1)? (1) (2) (3) (4)

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Type 4: Prism, angle of deviation, minimum deviation

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10) The minimum angle of deviation for a prism of refractive index 1.732 is equal to its refracting angle. What is the angle of prism? (1)40 0 (2) 45 0 (3) 60 0 (4) 30 0

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In this case A = D A/2 =30 0 Or A=60 o

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11) A ray of light is incident on one refracting face of a prism of angle 75 0. It passes through the prism and is incident on the other face at critical angle. If the refractive index of the material of the prism is √2, then the angle of incidence on the first face is (1)30 0 (2) 45 0 (3) 60 0 (4) 75 0

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C = 45 0 r1r1 C 75 0 We know that r 1 + C =75 0 r 1 =30 0

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Type 5: Small angled prism, angular dispersion and dispersive power Deviation Angular dispersion Dispersive power In case of C D F line

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12) The dispersive power of the material of the prism for which refractive index for violet and red colours are n v = 1.524, n r = 1.514 respectively is (1) 0.025 (2) 0.034 (3) 0.019 (4) 0.015

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Dispersive power is given by

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Type 6: Combination of Prisms Dispersion with out deviation Deviation with out dispersion

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13) A crown glass prism of 6 0 is cemented with a flint glass prism to form a pair which produces dispersion without deviation. If the refractive index of the crown glass prism is 1.52 and that of flint glass 1.66, then the angle of flint glass pair should be (1)4.73 0 (2) 5.73 0 (3) 6.73 0 (4) 7.73 0

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Condition for dispersion with out deviation is

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Conceptual questions

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14) Light appears to travel in straight line because (1)The frequency of light is very small (2) Light consists of very small particles (3) The wavelength of light is very small (4) The velocity of light is different for different colours.

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15) When light is refracted through a prism, maximum deviation occurs when the following conditions are satisfied (i) the ray is incident grazing the first face (ii) the ray emerges out grazing its second face Options (1)Only in case (i)(2) Only in case (ii) (3) In both the cases(4) Not under these cases

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16) A man is swimming underwater with undisturbed surface. Looking up at a bright sky through the water, he will see (1)a bright patch directly above whose angular size is independent of the depth of the swimmer (2)a shining surface of the water (3) just darkness (4) a bright patch directly above whose angular size depends upon the depth of the swimmer

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C C

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All the best Thank You

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