Title 28. Ray Optics hard.pdf ✅

1. An object of length 2.5 cm is placed at a distance of 1.5 f from a concave mirror where f is the magnitude of the focal length of the mirror. The length of the object is perpendicular to the principle axis. The length of the image is (a) 5 cm, erect (b) 10 cm, erect (c) 15 cm, erect (d) 5 cm, inverted 2. A convex mirror has a focal length f. A real object is placed at a distance f in front of it from the pole produces an image at (a) Infinity (b) f (c) f / 2 (d) 2f 3. Two objects A and B when placed one after another in front of a concave mirror of focal length 10 cm from images of same size. Size of object A is four times that of B. If object A is placed at a distance of 50 cm from the mirror, what should be the distance of B from the mirror (a) 10 cm (b) 20 cm (c) 30 cm (d) 40 cm 4. A square of side 3 cm is placed at a distance of 25 cm from a concave mirror of focal length 10 cm. The centre of the square is at the axis of the mirror and the plane is normal to the axis. The area enclosed by the image of the wire is (a) 4 cm2 (b) 6 cm2 (c) 16 cm2 (d) 36 cm2 5. A convex mirror of focal length 10 cm is placed in water. The refractive index of water is 4/3. What will be the focal length of the mirror in water (a) 10 cm (b) 40/3 cm (c) 30/4 cm (d) None of these 6. A candle flame 3 cm is placed at distance of 3 m from a wall. How far from wall must a concave mirror be placed in order that it may form an image of flame 9 cm high on the wall (a) 225 cm (b) 300 cm (c) 450 cm (d) 650 cm 7. A thin rod of length f / 3 lies along the axis of a concave mirror of focal length f. One end of its magnified image touches an end of the rod. The length of the image is (a) f (b) f 2 1 (c) 2 f (d) f 4 1 8. 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 9. A beam of monochromatic blue light of wavelength 4200 Å in air travels in water ( = 4 / 3) . Its wavelength in water will be (a) 2800 Å (b) 5600 Å (c) 3150 Å (d) 4000 Å 10. On a glass plate a light wave is incident at an angle of 600 . If the reflected and the refracted waves are mutually perpendicular, the refractive index of material is (a) 2 3 (b) 3 (c) 2 3 (d) 3 1 11. Consider the situation shown in figure. Water       = 3 4  w is filled in a breaker upto a height of 10 cm. A plane mirror fixed at a height of 5 cm from the surface of water. Distance of image from the mirror after reflection from it of an object O at the bottom of the beaker is (a) 15 cm (b) 12.5 cm (c) 7.5 cm (d) 10 cm 12. The wavelength of light in two liquids 'x' and 'y' is 3500 Å and 7000 Å, then the critical angle of x relative to y will be (a) 600 (b) 450 (c) 300 (d) 150 13. A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index  = 1.5) making an incidence angle of 600 on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to traverse the straight fiber of length 1 km (a) 3.33  sec (b) 6.67  sec (c) 5.77 sec (d) 3.85  sec 14. A glass prism of refractive index 1.5 is immersed in water ( = 4 / 3) . A light beam incident normally on the face AB is totally reflected to reach the face BC if (a) sin  8 / 9 (b) 2 / 3  sin  8 / 9 (c) sin  2 / 3 (d) cos  8 / 9 15. A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive indices of the material of the prism for the above red, green and blue wavelength are 1.39, 1.44 and 1.47 respectively. The prism will (a) Separate part of red colour from the green and the blue colours (b) Separate part of the blue colour from the red and green colours (c) Separate all the colours from one another (d) Not separate even partially any colour from the other two colours 45° B A  C
16. An air bubble in a glass slab ( = 1.5) is 6 cm deep when viewed from one face and 4 cm deep when viewed from the opposite face. The thickness of the glass plate is (a) 10 cm (b) 6.67 cm (c) 15 cm (d) None of these 17. Figure given below shows a beam of light converging at point P. When a concave lens of focal length 16 cm is introduced in the path of the beam at a place O shown by dotted line such that OP becomes the axis of the lens, the beam converges at a distance x from the lens. The value x will be equal to (a) 12 cm (b) 24 cm (c) 36 cm (d) 48 cm 18. A convex lens of focal length 40 cm is an contact with a concave lens of focal length 25 cm. The power of combination is (a) – 1.5 D (b) – 6.5 D (c) + 6.5 D (d) + 6.67 D 19. A combination of two thin lenses with focal lengths 1 f and 2 f respectively forms an image of distant object at distance 60 cm when lenses are in contact. The position of this image shifts by 30 cm towards the combination when two lenses are separated by 10 cm. The corresponding values of 1 f and 2 f are (a) 30 cm, – 60 cm (b) 20 cm, – 30 cm (c) 15 cm, – 20 cm (d) 12 cm, – 15 cm 20. A thin double convex lens has radii of curvature each of magnitude 40 cm and is made of glass with refractive index 1.65. Its focal length is nearly (a) 20 cm (b) 31 cm (c) 35 cm (d) 50 cm 21. A spherical surface of radius of curvature R separates air (refractive index 1.0) from glass (refractive index 1.5). The centre of curvature is in the glass. A point object P placed in air is found to have a real image Q in the glass. The line PQ cuts the surface at a point O and PO = OQ . The distance PO is equal to (a) 5 R (b) 3 R (c) 2 R (d) 1.5 R 22. The distance between an object and the screen is 100 cm. A lens produces an image on the screen when placed at either of the positions 40 cm apart. The power of the lens is (a) 3 D (b) 5 D (c) 7 D (d) 9 D 23. Shown in figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length +20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is (a) + 80 cm (b) – 80 cm (c) – 24 cm (d) – 100 cm 24. A concave lens of focal length 20 cm placed in contact with a plane mirror acts as a (a) Convex mirror of focal length 10 cm (b) Concave mirror of focal length 40 cm (c) Concave mirror of focal length 60 cm (d) Concave mirror of focal length 10 cm 25. A candle placed 25 cm from a lens, forms an image on a screen placed 75 cm on the other end of the lens. The focal length and type of the lens should be (a) + 18.75 cm and convex lens (b) – 18.75 cm and concave lens (c) + 20.25 cm and convex lens (d) – 20.25 cm and concave lens 26. A convex lens forms a real image of an object for its two different positions on a screen. If height of the image in both the cases be 8 cm and 2 cm, then height of the object is (a) 16 cm (b) 8 cm (c) 4 cm (d) 2 cm 27. A convex lens produces a real image m times the size of the object. What will be the distance of the object from the lens (a) f m m       + 1 (b) (m − 1)f (c) f m m       − 1 (d) f m + 1 28. An air bubble in a glass sphere having 4 cm diameter appears 1 cm from surface nearest to eye when looked along diameter. If a  g = 1.5 , the distance of bubble from refracting surface is (a) 1.2 cm (b) 3.2 cm (c) 2.8 cm (d) 1.6 cm 29. The sun's diameter is m 9 1.4 10 and its distance from the earth is m 11 10 . The diameter of its image, formed by a convex lens of focal length 2m will be (a) 0.7 cm (b) 1.4 cm (c) 2.8 cm (d) Zero (i.e. point image) 30. Two point light sources are 24 cm apart. Where should a convex lens of focal length 9 cm be put in between them from one source so that the images of both the sources are formed at the same place (a) 6 cm (b) 9 cm (c) 12 cm (d) 15 cm Lens Liquid O 12 cm P
31. There is an equiconvex glass lens with radius of each face as R and = 3 / 2 a  g and a  w = 4 / 3 . If there is water in object space and air in image space, then the focal length is (a) 2R (b) R (c) 3 R/2 (d) 2 R 32. When light rays are incident on a prism at an angle of 450 , the minimum deviation is obtained. If refractive index of the material of prism is 2 , then the angle of prism will be (a) 300 (b) 400 (c) 500 d) 600 33. Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism. The angle of prism is (cos 41 = 0.75) o (a) 620 (b) 410 (c) 820 (d) 310 34. Angle of glass prism is 600 and refractive index of the material of the prism is 1.414,then what will be the angle of incidence, so that ray should pass symmetrically through prism (a) 380 61' (b) 350 35' (c) 450 (d) 530 8' 35. A prism ( = 1.5) has the refracting angle of 300 . The deviation of a monochromatic ray incident normally on its one surface will be (sin 48 36' = 0.75) o (a) 180 36' (b) 200 30' (c) 180 (d) 22o 1' 36. Angle of a prism is 300 and its refractive index is 2 and one of the surface is silvered. At what angle of incidence, a ray should be incident on one surface so that after reflection from the silvered surface, it retraces its path (a) 300 (b) 600 (c) 450 (d) sin 1.5 −1 37. A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to 3/4 of the angle of the prism. The angle of deviation is (a) 450 (b) 390 (c) 200 (d) 300 38. Two identical prisms 1 and 2, each will angles of 300 , 600 and 900 are placed in contact as shown in figure. A ray of light passed through the combination in the position of minimum deviation and suffers a deviation of 300 . If the prism 2 is removed, then the angle of deviation of the same ray is (a) Equal to 150 (b) Smaller than 300 (c) More than 150 (d) Equal to 300 39. A prism having an apex angle 40 and refraction index 1.5 is located in front of a vertical plane mirror as shown in figure. Through what total angle is the ray deviated after reflection from the mirror (a) 1760 (b) 40 (c) 1780 (d) 20 40. A ray of light is incident to the hypotenuse of a right-angled prism after travelling parallel to the base inside the prism. If  is the refractive index of the material of the prism, the maximum value of the base angle for which light is totally reflected from the hypotenuse is (a)         −  1 sin 1 (b)         −  1 tan 1 (c)        −  −   1 sin 1 (d)         −  1 cos 1 41. If the refractive indices of crown glass for red, yellow and violet colours are 1.5140, 1.5170 and 1.5318 respectively and for flint glass these are 1.6434, 1.6499 and 1.6852 respectively, then the dispersive powers for crown and flint glass are respectively (a) 0.034 and 0.064 (b) 0.064 and 0.034 (c) 1.00 and 0.064 (d) 0.034 and 1.0 42. Flint glass prism is joined by a crown glass prism to produce dispersion without deviation. The refractive indices of these for mean rays are 1.602 and 1.500 respectively. Angle of prism of flint prism is 100 , then the angle of prism for crown prism will be (a) 12 2.4' o (b) 12 4' o (c) o 1.24 (d) 120 43. A man can see the objects upto a distance of one metre from his eyes. For correcting his eye sight so that he can see an object at infinity, he requires a lens whose power is or A man can see upto 100 cm of the distant object. The power of the lens required to see far objects will be (a) +0.5 D (b) +1.0 D (c) +2.0 D (d) –1.0 D 44. A man can see clearly up to 3 metres. Prescribe a lens for his spectacles so that he can see clearly up to 12 metres (a) – 3/4 D (b) 3 D (c) – 1/4 D (d) – 4 D 45. The diameter of the eye-ball of a normal eye is about 2.5 cm. The power of the eye lens varies from (a) 2 D to 10 D (b) 40 D to 32 D (c) 9 D to 8 D (d) 44 D to 40 D 46. The resolution limit of eye is 1 minute. At a distance of r from the eye, two persons stand with a lateral separation of 3 metre. For the two persons to be just resolved by the naked eye, r should be (a) 10 km (b) 15 km (c) 20 km (d) 30 km 2° 2° 2° 4° 30o 30o 60o 60 90 o o 90o
47. Two points separated by a distance of 0.1 mm can just be resolved in a microscope when a light of wavelength 6000 Å is used. If the light of wavelength 4800 Å is used this limit of resolution becomes (a) 0.08 mm (b) 0.10 mm (c) 0.12 mm (d) 0.06 mm 48. In a compound microscope, the focal lengths of two lenses are 1.5 cm and 6.25 cm an object is placed at 2 cm form objective and the final image is formed at 25 cm from eye lens. The distance between the two lenses is (a) 6.00 cm (b) 7.75 cm (c) 9.25 cm (d) 11.00 cm 49. The focal lengths of the objective and the eye-piece of a compound microscope are 2.0 cm and 3.0 cm respectively. The distance between the objective and the eye-piece is 15.0 cm. The final image formed by the eye-piece is at infinity. The two lenses are thin. The distances in cm of the object and the image produced by the objective measured from the objective lens are respectively (a) 2.4 and 12.0 (b) 2.4 and 15.0 (c) 2.3 and 12.0 (d) 2.3 and 3.0 50. The focal lengths of the objective and eye-lens of a microscope are 1 cm and 5 cm respectively. If the magnifying power for the relaxed eye is 45, then the length of the tube is (a) 30 cm (b) 25 cm (c) 15 cm (d) 12 cm 51. If the focal lengths of objective and eye lens of a microscope are 1.2 cm and 3 cm respectively and the object is put 1.25 cm away from the objective lens and the final image is formed at infinity, then magnifying power of the microscope is (a) 150 (b) 200 (c) 250 (d) 400 52. The magnifying power of an astronomical telescope is 8 and the distance between the two lenses is 54cm. The focal length of eye lens and objective lens will be respectively (a) 6 cm and 48 cm (b) 48 cm and 6 cm (c) 8 cm and 64 cm (d) 64 cm and 8 cm 53. If an object subtend angle of 20 at eye when seen through telescope having objective and eyepiece of focal length fo = 60 cm and f e = 5 cm respectively than angle subtend by image at eye piece will be Q (a) 160 (b) 500 (c) 240 (d) 100 54. The focal lengths of the lenses of an astronomical telescope are 50 cm and 5 cm. The length of the telescope when the image is formed at the least distance of distinct vision is (a) 45 cm (b) 55 cm (c) 6 275 cm (d) 6 325 cm 55. The diameter of moon is km 3 3.5 10 and its distance from the earth is km 5 3.8 10 . If it is seen through a telescope whose focal length for objective and eye lens are 4 m and 10 cm respectively, then the angle subtended by the moon on the eye will be approximately (a) 150 (b) 200 (c) 300 (d) 350 56. A telescope has an objective lens of 10 cm diameter and is situated at a distance one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is 5000 Å, is of the order of (a) 0.5 m (b) 5 m (c) 5 mm (d) 5cm 57. A compound microscope has a magnifying power 30. The focal length of its eye-piece is 5 cm. Assuming the final image to be at the least distance of distinct vision. The magnification produced by the objective will be (a) +5 (b) – 5 (c) + 6 (d) – 6 58. A glass prism of refractive index 1.5 is immersed in water (R.I. = 4/3). The beam of light incident normally on the face AB is totally reflected to reach the face BC, if C  B A (a) Sin  8/9 (b) Sin < 2/3 (c) 2/3 < Sin < 8/9 (d) None of these 59. Two beams of light are incident normally on water (R.I. = 4/3). If the beam 1 passes through a glass of height h as shown in the figure, the time difference for both the beams for reaching the bottom is 1 h 2 h’ glass (a) Zero (b) 6C h (c) C 6 h (d) 6C h 60. A beaker containing liquid is placed on a table underneath a microscope with can be moved along a vertical scale. The microscope is focused, through the liquid into a mark on the table when the reading on the scale is a. It is next focused on the upper surface of the liquid and the reading be b. More the liquid is added and the observations are repeated, the corresponding readings are C and d. The refractive index of the liquid is (a) d c b a d b − − + − (b) d c b a b d − − + − (c) d b d c b a − − − + (d) a b c d d b + − − −