OPTICS-03- ObjECTIVE SOlVED

SOLVED OBJECTIVE PROBLEMS Problems 1. In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wave-length  ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass plate is (a) 2 (b) 2 / 3 (c) Ans. (a)  / 3 (d)  . Solution: Shift  D ( 1)t  D d d t    2  1 Problems 2. Two plane mirrors A and B are aligned parallel to each B other, as shown in the figure. A light ray is incident at an angle of 30º at a point just inside one end of A. The plane of incidence coincides with the plane of the fig- ure. The maximum number of time the ray undergoes reflections (including the first one) before it emerges out is (a) 28 (b) 30 (c) 32 (d) 34. Ans. (b) Solution: No. of reflections   30 . Problems 3. A ray of light passes through four transparent media with refractive indices 1 , 2 , 3 and 4 as shown in the fig- ure, the surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have (a) (c) Ans. (d) 1  2 3  4 (b) (d) 2  3 4  1 . Solution: According to Snell’s Law, sin  =constant which gives 1  4 . Problems 4. A diminished image of an object is to be obtained on a screen 1.0 m away from it. This can be achieved by approximately placing (a) a convex mirror of suitable focal length (b) a concave mirror of suitable focal length (c) a convex lens of focal length less than 0.25 m (d) a concave lens of suitable focal length. Ans. (b), (c) Solution: Image can be formed on the screen if it is real. Real image of reduced size can be formed by a concave mirror or a convex lens. Let u = 2f + x, then 1  1  1 u v f 1  1  1 2f  x v f 1  1  1  f  x v f 2f  x f (2f  x) v  f (2f  x) f  x It is given that u + v = lm 2f  x  f (2f  x)  (2f    f   lm f  x f (2f  x)2  x) 1  f  x  or f  x lm or (2f  x)2  (f  x) This will be true only when f < 0.25 m. Problems 5. A ray of light traveling in a transparent medium falls on a surface separating the medium from air at an angle of incidence of 45º. The ray undergoes total internal reflection. If n is the refractive index of the medium with respect to air, select the possible value(s) of n from the following (a) 1.3 (b) 1.4 (c) 1.5 (d) 1.6. Ans. (c), (d) Solution: Here 45º > c sin 45º > sin c   1 n  n  Problems 6. A ray of light passes through an equilateral prism such that the angle of incidence and the angle of emergence are both equal to 3/4th of the angle of prism. The angle of minimum deviation is (a) 15º (b) 30º (c) 45º (d) 60º. A Ans. (b) Solution: Givne A = 60º i  i  3 A  45º 4  i  i  A   or 90º = 60º +     30º Note that i  i is the condition for minimum deviation. Hence   30º  min . Problems 7. A lens of focal length f projects m times magnified image of an object on a screen. The distance of the screen from the lens is (a) f (m 1) (b) f (m 1) (c) f (m 1) (d) f (m 1) . Ans. Solution: (d) Image will be real. We know that 1  1  1 f v u v  1 v f u v  1 m f  v  f (m 1) . [ u is negative] Problems 8. A thin equiconvex lens of refractive index 3/2 and radius of curvature 30 m is put in water (refractive index  4 ). Its focal length is 3 (a) 0.15 m (b) 0.30m (c) 0.45 m (d) 1.20 m. Ans. (d) 1   1 1 1  1  Solution: f    R R   2  1 2  1   3 / 2 1 1  1  f  4 / 3  0.3 0.3     or 1   9 1 2  f  8  0.3     or 1  1  2 f 8 0.3 or f  1.20 m . Problems 9. A 16 cm long image of an object is formed by a convex lens on a screen. On moving the lens towards the screen, without changing the positions of the object and the screen, a 9 cm long image is formed again on the screen. The size of the object is (a) 9 cm (b) 11 cm (c) 12 cm (d) 13 cm. Ans. (c) Solution: y   16  9  4 3  12 cm . Problems 10. Two lenses, one concave and the other convex of same power are placed such that their principal axes coincide. If the separation between the lenses is x, then (a) real image is formed for x = 0 only (b) real image is formed for all values of x (c) system will behave like a glass plate for x = 0 (d) virtual image is formed for all values of x other than zero. Ans. (b), (c) Solution: 1  1  1  x f f1 f2 f1f2 1  1  1  x f f f f 2 1 x 2 1 1 for x  0, f    f  0 for every x. Hence for x = 0, system will behave like a glass plate. Problems 11. When a beam of light with wavelength,   6000 A , traveling in air, enters a glass medium whose refractive index is 1.5 then (a) frequency of light remains constant (b) velocity of light increases by 1.5 times (c) frequency of light increases by 1.5 times (d) wavelength () Ans. (a), (d) of light decreases by 1.5 times. Solution: (i) When a beam of light enters from one medium to other, its frequency remains un- changed. (ii) V = n and   c v 1.5  n1 n2 or 1.5  1 2 or   1 2 1.5 Hence wavelength decreases by 1.5 times. Problems 12. A ray of light falls on a transparent glass slab with refractive index (relative to air) of 1.62. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is: (a) tan1(1.62) (b) sin1(1.62) (c) Ans. (a) cos1(1.62) (d) none of these. Solution: we know that   sin i sin r or r = 90 - i and i  r  90º sin i sin(90  i)  tan i or i  tan1()  tan1(1.62) . Problem 13. An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is 3h and its radius is h. When the beaker is filled with a liquid up to a height 2h, he can see the lower end of the rod. Then the refractive index of the liquid is (a) 5/2 (b) (c) Ans. (b) Solution: sin i  1 (d) 3/2. sin r  x x2  4h2  1 2h  x  (2h  x)2  h2 …(i) q0rt h h x r h 2h-x Eye sin r   x h 2 …(ii) Using (i) and (ii),   Problems 14. In a Young’s double slit experiment, 12 fringes are observed to be formed in a certain seg- ment of the screen when light of wavelength 600 nm is used. If the wavelength of light is changed to 400 nm, number of fringes observed in the same segment of the screen is given by (a) 12 (b) 18 (c) 24 (d) 30. Ans. (b) Solution: Number of fringes = We know that, length of region fringe width Fringe width  wavelength 12  600  x  400 x  18 . Problems 15. Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is / 2 at point A and  at point B. Then the difference between resultant intensities at A and B is (a) 2I (b) 4I (c) 5I (d) 7I. Ans. (b) Solution: I  I  4I  2(I  4I)1/ 2 cos At A,    / 2  IA  5I At B,     IA  IB  4I . IB  I