OPTICS-05-OBJECTIVE UNSOLVED LEVEL - I

OBJECTIVE UNSOLVED LEVEL - I 1. Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams R1 R2 (a) R1  R 2 (b) R (c) R R (d) R . 2. A point source of light B is placed at a distance L in front of the B centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. The greatest distance over which he can see the image of the light source of the mirror is (a) d/2 (b) d L (c) 2d (d) 3d. 2L 3. A concave mirror is placed on a horizontal table, with its axis directed vertically upwards. Let O be the pole of the mirror and C its centre of curvature. A point object is placed at C. It has a real image, also located at C. If the mirror is now filled with water, the image will be (a) real and will remain at C (b) real and located at a point between C and  (c) virtual and located at a point between C and O (d) real and located at a point between C and O. 4. A 4.0 cm thick water layer (  4 / 3) rests on a 6.0 cm layer of CCl4 (  1.5) in a tank. How far below the water surface, viewed normally from above, does the bottom of the tank seem to be (a) 7.0 cm (b) 8.0 cm (c) 9.0 cm (d) 10.0 cm. 5. The velocity of light in a medium is half its velocity in air. If a ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is (a) 15º (b) 30º (c) 45º (d) 60º. 6. A parallel beam of light is incident on a crown glass convex lens of focal length f. A flint glass concave lens of the same focal length is placed in contact with it. The image will now be formed at (a) f (b) between f and 2f (c) 2f (d) infinity. 7. A thin double convex lens has radii of curvature each of magnitude 40 cm and is made of glass with μ  1.5 . The focal length of the lens is (a) 30 cm (b) 31 cm (c) 40 cm (d) 41 cm. 8. The refractive indices of a medium for two waves A and B are n1 and which will travel faster in the medium? (a) A (b) B n2 respectively. If n1  n2 , (c) Both A and B (d) Neither of the two waves. 9. The refractive index of diamond is 2.0. the velocity of light in diamond in cm/s is (a) (c) 6 1010 1.5108 (b) (d) 1.5 1010 6 108 . 10. In a double slit experiment, instead of taking slits of equal widths, one slit is made twice as wide as the other. Then, in the interference pattern (a) the intensities of both the maxima and the minima increase (b) the intensity of the maxima increases and the minima has zero intensity (c) the intensity of the maxima decreases and that of the minima increases (d) the intensity of the maxima decreases and the minima has zero intensity. 11. A hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids L1 or L2 having refracting indices n1 and n2 respectively ( n2  n1  1) . The lens will diverge a parallel beam of light if it is filled with (a) air and placed in air. (b) air and immersed in L1 (c) L1 and immersed in L2 (d) L2 and immersed in L1 . 12. A thin slice is cut out of a glass cylinder along a plane parallel to its axis. The slice is placed on a flat glass plate as shown. The ob- served interference fringes from its combination shall be (a) straight (b) circular (c) Equally spaced (d) having fringe spacing which increase as we go outwards. 13. A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refrac- tive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have real image Q in the glass. The line PQ cuts the surface at a point O, PO = OQ. The distance PO is equal to (a) 5R (b) 3R (c) 2R (d) 15R. 14. Diameter of convex surface of plano-convex lens is 6 cm and thickness at the centre is 3 mm. If the speed of light in the material of the lens is 2 108 m/s, the focal length of the lens is : (a) 15 cm (b) 20 cm (c) 30 cm (d) 10 cm. 15. A luminous point is moving at speed v0 towards a spherical mirror, along its axis. Then the speed at which the image of this point object is moving is given by (with R = radius of curvature and u = object distance): (a) v  v (b) v  v  R  i 0 i 0  2u  R   2u  R   R 2 (c) vi  v0  R  (d) vi  v0  2u  R  .     OBJECTIVE UNSOLVED LEVEL - II 1. A given ray of light suffers minimum deviation in an equi- lateral prism P. Additional prisms Q and R of identical shape and of the same material as P are now added as shown in the figure. The ray will now suffer (a) greater deviation (b) no deviation P Q R (c) same deviation as before (d) total internal reflection. 2. A diverging beam of light from a point source S having divergence S angle  , falls symmetrically on a glass slab as shown. the angles of incidence of the two extreme rays are equal. If the thickness of the glass slab is t and the refractive index n, then the divergence angle of the emergent beam is (a) zero (b)  l (b) (b) sin1 (1/ n) (d) 2sin1 (1/ n) . 3. An isosceles prism of angle 120º has a refractive index of . Two parallel monochromatic rays enter the prism parallel to each other in air as shown. the rays emerging from the opposite faces (a) are parallel to each other (b) are diverging (c) make an angle 30º with each other (d) make an angle 60º with each other. 4. Light is incident from vacuum on the surface of a medium of refractive index  . If the angle of incidence obeys the relation i  tan1 () , the angle between the reflected and refracted rays is (a) 30º (b) 45º (c) 90º (d) 135º. 5. A man has a concave shaving mirror of focal length 0.2 m. How far should the mirror be held from his face in order to give an image of two fold magnification? (a) 0.1 m (b) 0.2 m (c) 0.3 m (d) 0.4 m. 6. A small angled prism has its refracting angle A = 4º and refractive index  3 . It is placed with its 2 base horizontal in front of a vertical mirror. A horizontal ray of light passes through the prism and is reflected back from the mirror. By what angle the mirror should be rotated so that the reflected ray becomes horizontal? (a) 1º (b) 4º (c) 6º (d) 8º. 7. A light ray of frequency v and wavelength  enters a liquid of refractive index in the liquid with 3 2 . The ray travels (a) frequency v and wavelength (b) frequency v and wavelength  2     3    (c) frequency v and wavelength  (d) frequency  3  v   and wavelength  . 8. A parallel beam of light falls normally on the plane surface of a plano convex lens of refractive index 3/2. If the radius of the curved surface of the lens is 20 cm, the beam will be focused at which of the following distances from the lens? (a) 20 cm (b) 30 cm (c) 40 cm (d) 50 cm. 9. In an interference arrangement similar to Young’s double-slit ex- periment, the slits S and S are illuminated with coherent micro- d/2 1 2 wave sources, each of frequency 106 Hz. The sources are syn- chronized to have zero phase difference. The slits are separated by d/ a distance d = 150.0 m. The intensity I() is measured as a func- tion of  , where  is defined as shown. If I0 intensity, then I() for 0    900 is given by is the maximum (a) I()  I0 / 2 for   30º (b) I()  I / 4 for   90o (c) I()  I0 / 4 for   0o (d) I() is constant for all values of  . 10. Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are in the ratio (a) 5 : 1 (b) 5 : 3 (c) 9 : 1 (d) 9 : 3. 11. A thin prism P1 with angle 4º and made from glass of refractive index 1.54 is combined with another thin prism P2 made from glass of refractive index 1.72 to produce dispersion without deviation. The angle of the prism P2 is (a) 5.33º (b) 4º (c) 3º (d) 2.6º. 12. A beam of light consisting of red, green and blue colours is incident on a right-angled prism as shown in figure. The refractive indices of the material of the prism for the above red, green and blue wave- lengths are 1.39, 1.44 and 1.47 respectively. The prism will (a) Separate part of the red colour from the green and blue colours. (b) Separate part of the blue colour from the red and green colour. (c) Separate all the three colour from one another. (d) Not separate even partially any colour from the other two colours. 13. A short linear object of length b lies along the axis of a concave mirror of focal length f at a distance u from the pole of the mirror. Size of the image is approximately equal to  u  f 1/ 2  f 1/ 2 (a) b f  (b) b u  f       u  f   f 2 (c) b f  (d) b u  f  .     14. A rectangular glass slab ABCD, of refractive index n1 , is immersed in water of refractive index n2 (n1  n2 ) . A ray of light is incident at the surface AB of the stab as shown. The maximum value of the angle of incidencemax , such that the ray comes out only from the other surface CD is given by max sin1  n1  1 n2  1   1 1  (a) n cossin n  (b) sin n1 cossin n2   2  1     sin1  n1  sin1  n2  (c)    2  (d)   .  1  15. Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio (a) 25 : 1 (b) 5 : 1 (c) 9 : 4 (d) 625 : 1.