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Ray Optics and Wave Optics 1. A uniform horizontal light beam is incident upon a prism (quarter cylindrical shape) as shown in the figure. The radius of the prism is R and the cylinder material has a refractive index 2 √3 . A patch on the table for a distance d from the surface of the cylinder is unilluminated. Find the value of d in terms of R. (A) R/2 (B) R (C) √3R (D) 2R 2. In the figure shown, the focal length of the two thin convex lenses is the same f. They are separated by a horizontal distance 3f and their optical axis are displaced by a vertical separation ' d ' (d << f), as shown. Taking the origin of coordinates O at the centre of the first lens, the x and y coordinates of the point where a parallel beam of rays coming from the left finally get focused, are given by : (A) (5f, 2d) (B) (6f, d/2) (C) (4f, 2d) (D) (2f, 4d) 3. A convex lens of focal length 15 cm is placed at the origin with its optical axis coinciding with the x- axis. A ray of light given by y = − x 3 + 1 is incident on the lens. The equation of refracted ray is ( x and y are in cm ) (A) y = −0.2x + 3 (B) y = −0.3x + 2 (C) y = −0.4x + 1 (D) y = −0.1x + 4 4. A double slit, S1 − S2 is illuminated by a light source S emitting light of wavelength λ. The slits are separated by a distance d. A plane mirror is placed at a distance D in front of the slits and a screen is placed at a distance 2D behind the slits. The screen receives light reflected only by the plane mirror. The fringe-width of the interference pattern on the screen is (A) Dλ d (B) 2Dλ d (C) 3Dλ d (D) 4Dλ d 5. A light ray is reflected by a mirror. If unit vectors along the incident and normal direction are Iˆ = 1 √3 iˆ − 1 √3 jˆ + 1 √3 kˆ and Nˆ = iˆ, then unit vector, Rˆ
along reflected direction is. (A) 1 √7 (√2iˆ + √2jˆ − √3kˆ ) (B) −1 √3 iˆ − 1 √3 jˆ − 1 √3 kˆ (C) − 1 √3 iˆ − 1 √3 jˆ + 1 √3 kˆ (D) 1 √3 iˆ + 1 √3 jˆ + 1 √3 kˆ 6. A portion of straight glass rod of diameter 4 cm and refractive index 1.5 is bent into an arc of circle of radius Rcm and a parallel beam of light is incident on it as shown in the figure. Find the smallest R which permits all the light to pass around the arc. (A) 6 cm (B) 12 cm (C) 24 cm (D) None of these 7. A ray of light l is incident on a thin film. Two reflected rays R1 and R2 and two transmitted rays T1 and T2 for the incident ray l are shown in the figure. If the rays R2 and T2 undergoes a phase change of π due to difference in refractive index of the mediums, then select the correct order of refractive indeces. (A) μ1 > μ2 > μ3 (B) μ1 < μ2 < μ3 (C) μ1 > μ2 < μ3 (D) μ1 < μ2 > μ3 8. White light is used in a Young's double slit experiment. The slit width is d and the separation between the slit plane and the screen plane is D(D >> d). Some wavelength are missing on the point on the screen in front of both the slits. Select the missing wavelength. (A) d 2 2D (B) d 2 4D (C) d 2 3D (D) None of these 9. A ray beam of width 1 cm is incident from air to air-water boundary at an angle of 45∘ . What is the width of the refracted beam in water? (Refractive index of water = √2 ) (A) 1 2 cm (B) 1 √2 cm (C) 1 cm (D) √3 √2 cm 10. Two coherent narrow slits emitting wavelength λ in the same phase are placed at (0,0,0) and (3λ, 0,0) in an x − y − z space as shown in the figure. The light from the two slits interfere on a screen S which is parallel to y-z plane and is placed at a distance D(D > λ) from the origin. Find the distance y of the nearest point on the screen from the centre of the screen P, where intensity is equal to that at P (A) D (B) √3D (C) √5D 2 (D) √5D 11. A light ray incident along vector 2iˆ + 4jˆ + √5kˆ strikes on the x-z plane from medium I of refractive index √3 and enters into medium II of refractive index is μ2. The value of μ2 for which the value of angle of refraction becomes 90∘ , is : (A) 4√3 5
(B) 3√3 5 (C) 2√3 5 (D) √3 5 12. A point source of light ' O ' is kept on the principal axis of a thin plano-convex lens of radius of curvature 20 cm as shown. The refractive index of material of lens is 3/2, then medium towards right of plane surface is water of refractive index 4/3 and the medium on the left side of curved surface of lens is air. Considering only paraxial rays, the distance ' x ' of the point source ' O ' from the lens such that the rays become parallel on entering the water will be: n1 = 3/2 (A) 10 cm (B) 20 cm (C) 40 cm (D) None of these 13. The minimum value of refractive index n of a cylindrical solid rod placed in air, so that the light entering through the flat surface of the rod does not cross the curved surface of the rod is : (A) √3 2 (B) √2 (C) 2 (D) √3 14. In the figure shown in a YDSE, a parallel beam of light is incident on the slits from a medium of refractive index n1. The wavelength of light in this medium is λ1. A transparent slab of thickness ' t ' and refractive index n3 is put infront of one slit. The medium between the screen and the plane of the slits is n2. The phase difference between the light waves reaching point ' O ' (symmetrical, relative to the slits) is : (A) 2π n1λ1 (n2 − n3 )t (B) 2π λ1 (n3 − n2 )t (C) 2πn1 22λ1 ( n3 n2 − 1) t (D) 2πn1 λ1 (n3 − n2 )t 15. In a Young's double slit experiment D equals the distance of screen and d is the separation between the slits. The distance of the nearest point to the central maximum where the intensity is same as that due to a single slit, is equal to (A) Dλ d (B) Dλ 2d (C) Dλ 3d (D) 2Dλ MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. The gap between the slit plane and the screen is filled with water and a parallel beam of monochromatic light of wavelength, λ = 0.25 mm and the intensity I0 is incident at an angle 30∘ with the horizontal. A slab of thickness 0.5 mm and refractive index μs = 1.5 is placed before S1. Choose the correct option(s).
(A) central maxima is observed above O (B) central maxima observed below O (C) intensity at O is 4I0 (D) 3 rd order maxima is at O 17. If white light is used in a Young's double-slit experiment, (A) bright white fringe is formed at the centre of the screen (B) fringes of different colours are observed clearly only in the first order (C) the first-order violet fringe is closer to the centre of the screen than the first-order red fringe (D) the first-order red fringe is closer to the centre of the screen than the first-order violet fringe 18. In Young's double slit experiment two wavelengths of light are used simultaneously where λ2 = 2λ1. In the fringe pattern observed on the screen (A) maxima of wavelength λ2 can coincide with minima of wavelength λ1 (B) fringe width of λ2 will be double that of fringe width of λ1 and the nth order maxima of λ2 will coincide with 2n order maxima of λ1. (C) n th order maxima of λ2 will coincide with 2n th order maxima of λ1. (D) None of the above 19. A particle moves towards a concave mirror of focal length 30 cm along its axis and with a constant speed of 4 cm/sec. At the instant the particle is 90 cm from the pole (A) velocity of image is 1 cm/sec (B) velocity of image w.r.t. particle is 5 cm/sec (C) particle and image move towards each other (D) as the particle approaches pole, velocity of image increases 20. The minimum value of d so that there is a dark fringe at O is dmin. For the value of dmin, the distance at which the next bright fringe is formed is x. Then : (A) dmin = √λD (B) dmin = √ λD 2 (C) x = dmin 2 (D) x = dmin 21. Two point monochromatic and coherent sources of light of wavelength λ are each placed as shown in the figure below. The initial phase difference between the sources is zero O. (D ≫ d). Select the correct statement(s) : (A) If d = 7λ 2 ,O will be minima (B) If d = λ, only one maxima can be observed on screen (C) If d = 4.8λ, then a total 10 minimas would be there on screen (D) If d = 5λ 2 , then intensity at O would be minimum 22. The slit 1 of a Young's double slit experiment is wider than slit 2, so that the light from slits are given as A1 = A0sin ωt and A2 = 3A0sin (ωt + π 3 ). Then resultant amplitude and intensity at a point where the path difference between them is zero, is A and t respectively, then : (A) A = √13A0 (B) A = 4A0 (C) I ∝ 16A0 2 (D) I ∝ 13A0 2 23. Two transparent parallel plates are stacked face to face. The plate whose thickness t1 = 4.5 cm has a refractive index n1 = 3 2 while the other plate whose thickness t2 = 2 cm has a refractive index n2 = 4 3 .