REFRACTION OF LIGHT VERY SHORT ANSWER QUESTIONS Q-1. The earth takes 24 h to rotate once about its axis. How much time does the sun take to shift by 1 0 when viewed from the earth? Q-2. What is the maximum angle of refraction when a ray of light is refracted from glass into air? Q-3. A ray of light is incident normally on a glass slab. What is the angle of refraction? Q-4. What is the power of the combination of a convex lens and a concave lens of the same focal length? Q-5. How is power of a lens related to its focal length? Q-6. Can the absolute refractive index of a medium be less than unity? Q-7. To a fish under water viewing obliquely a fisherman standing on the bank of a lake, does the man look taller or shorter than what actually he is? Q-8. A beam of light is converging towards a certain point. A parallel sided glass plate is introduced in the path of the converging beam. How will the point of convergence be shifted? Q-9. What should be the position of an object relative to biconvex lens so that this lens behaves like a magnifying glass? Q-10. What happens to the frequency when light passes from one medium to another? Q-11. What is critical angle for a material of refractive index 2? Q-12. Does critical angle depend on colour of light? Q-13. What is the focal length and power of a plane glass plate? Q-14. A convex lens is placed in a medium in which it behaves as an ordinary plate. What is the refractive index of the medium relative to the lens? Q-15. What type of lens is an air bubble inside water? Q-16. What is lens maker s formula? Q-17. What is the ratio of velocities of two light waves travelling in vacuum and having wave lengths 4000 Ǻ and 8000 Ǻ? 1
Q-18. A lens when immersed in a transparent liquid becomes invisible. Under what condition does it happen? Q-19. Define critical angle for total internal reflection. Q-20. Which of the following does not change when light goes from one medium to another? Frequency, wavelength, speed and intensity. Q-21. What is refraction? Q-22. What is the unit of power of lens? Q-23. What is the physical principle on which the working of optical fibre is based? Q-24. An object is placed at the focus of a concave lens. Where will its image be formed? Q-25. Which of the two main parts of an optical fibre has a higher value of refractive index? Q-26. What happens to the focal length of a convex lens when immersed in water? Q-27. State Snell s law of refraction of light. Q-28. What is the basic cause of refraction of light? Q-29. A double convex lens, made from a material of refractive index μ 1, is immersed in a liquid of refractive index μ 2 where μ 2 > μ 1. What change, if any, would occur in the nature of the lens? SHORT ANSWER QUESTIONS Q-30. A magician during a show makes a glass lens n = 1.47 disappear in a trough of liquid. What is the refractive index of the liquid? Could the liquid be water? Q-31. What do you understand by the term superior mirage? Q-32. What do you understand by the term inferior mirage? Q-33. The image of a candle formed by a convex lens is obtained on a screen. Will full size of the image be obtained if the lower half of the lens is painted completely opaque? Q-34. Why goggles (Sun glasses) have zero power even through their surface are curved? Q-35. Explain why a convex lens behaves as a diverging lens when immersed in carbon disulphide? While the refractive index of glass in 1.5, the refractive index of carbon disulphide is 1.65. Q-36. Explain the shining of an air bubble in water. 2
Q-37. Show analytically from the lens equation that when the object is at the principal focus, the image is formed at infinity. Q-38. Use the lens equation to deduce algebraically the following : A concave lens produces a virtual and diminished image independent of the location of the object. Q-39. Use the lens equation to deduce algebraically the following : An object placed within the focus of a convex lens produces a virtual and enlarged image. Q-40. A 35 mm slide with a 24 mm 36 mm picture is projected on a screen placed 12 m from the slide. The image of the slide picture on the screen measures 1.0 m 1.5 m. Determine the location of the projection lens, and its focal length. Q-41. Why do we need a condensing lens at all? Can we not project a slide simply by illuminating it by a lamp and obtaining its magnified image on a screen? Q-42. For projecting the slide in Q. 40, how much should be the least diameter of the condensing lens? Where should the slide be placed relative to this lens? Q-43. The image of the source formed by the condensing lens should be located on the projection lens. Why? What is the preferred size of this image of the source? Explain. Q-44. The condensing lens converges light from the source on to the slide. Does that mean the image of the source is formed on the slide? If not, why not? Q-45. Consider a small portion of the image on the screen, say the lowermost portion. Does this portion get illumination only from the lowermost part of the source? Or only from the uppermost part of the source? Or from all points of the source? Explain. Q-46. The lens shown in Fig 17.86 is made of two different materials. A point object is placed on the principal axis of this lens. How many images will be obtained? 3
Q-47. A convex lens (refractive index μ l ) is immersed in a medium (refractive index μ m ). How would it behave if (i) μ l > μ m (ii) μ l < μ m? Q-48. Why the rising Sun appears bigger? Q-49. Q-50. Define focus and principal focus of a lens. Velocity of light in a liquid in a liquid is 1.5 10 8 m s -1 and in air, it is 3 10 8 m s -1. If a ray of light passes from this liquid into air, calculate the value of critical angle. Q-51. Watching the sunset on a beach, one can see the Sun for several minutes after it has actually set. Explain. Q-52. For the same angle of incidence, the angles of refraction in media P, Q and R are 35 0, 25 0, 15 0 respectively. In which medium will the velocity of light be minimum? Q-53. A convex lens is held in water. What would be the change in the focal length? Q-54. A convex lens forms the image of the sun at a distance of 10 cm. Where will be the image when (i) another lens of same power but double the aperture is used? (ii) another lens of same aperture but double the power is used? Q-55. On a hot summer day in a desert, one sees the reflected image of distant parts of the sky. (This is sometimes mistaken by the observer to be the reflection of the sky in some distant lake of water. This illusion is called a mirage.) Explain. Q-56. Where should an object be planed from a convex lens to form an image of the same size? Can it happen in the case of a concave lens? Q-57. Two concave lenses, each of focal length 30 cm, are placed in contact. What is the focal length of the compound lens? 4
Q-58. Why does a diamond sparkle with great brilliance? Q-59. Violet light is incident on a thin convex lens. If this light is replaced by red light, explain with reason, how the power of the lens would change. Q-60. A substance has critical angle of 45 0 for yellow light. What is its refractive index? Q-61. What is optical fibre? Q-62. The image of a candle is formed by a convex lens on a screen. The lower half of the lens is painted black to make it completely opaque. Draw ray diagram to show the image formation. How will this image be different from the one obtained when the lens is not painted black? Q-63. A right-angle prism is placed before an object in the two positions shown in Fig 17.88. The prism is made of crown glass with critical angle equal to 41 0. Trace the paths of two rays P and Q normal to the hypotenuse in (a), and parallel to the hypotenuse in (b). Q-64. Monochromatic light is refracted from air into glass of refractive index n. Find the ratio of wavelengths of the incident and refracted light. Q-65. Write two conditions necessary for total internal reflection to take place. SHORT ANSWER QUESTIONS Q-66. Explain why (a) A diamond glitters in a brightly lit room but not in a dark room. (b) A crack in window-pane appears silvery. (c) The bubbles of air rising up in a water tank appear silvery when viewed from top. 5
Q-67. One end of a cylindrical glass rod (μ = 1.5) of radius 1.0 cm is rounded in the shape of a hemisphere. The rod is immersed in water μ = 4 3 and an object is placed in the water along the axis of the rod at a distance of 8.0 cm from the rounded edge. Determine the location of the image of the object. Q-68. A ray of light suffers lateral displacement when refracted by a parallel-sided glass slab. Determine the condition for this lateral displacement to be maximum. What will be the maximum possible value of the lateral displacement? Q-69. Refer to Figs 17.91 (a), (b) and (c). Give relationship between μ 1 and μ 2 in each case. Q-70. Light falls from glass (μ = 1.5) to air. Find the angle of incidence for which the angle of deviation in 90 0. Q-71. A concave lens made of a material of refractive index μ g is immersed in a medium whose refractive index μ l is (i) greater than (ii) equal to (iii) less than μ g. When a parallel beam of light is incident on the lens, trace the path of the emergent rays in each of the above cases. Q-72. Three rays of light red (R), green (G) and blue (B) are incident on the face AB of a right-angled prism ABC. The refractive indices of the material of the prism for red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively. Trace the path of the rays through the prism. How will the situation change if these rays were incident normally on one of the faces of an equilateral prism? 6
Q-73. A double convex lens made of glass of refractive index 1.5 has both radii of curvature 20 cm each. Find the focal length of the lens. If an object is placed at a distance of 15 cm from this lens, find the position of the image formed. Q-74. The following data was recorded for values of object distance and the corresponding values of image distance in the experiment on study of real image formation by a convex lens of power +5D. One of these observations is incorrect. Identify this observation and give reason for your choice : S.No 1 2 3 4 5 6 Object distance (cm) Image distance (cm) 25 30 35 45 50 55 97 61 37 35 32 30 Q-75. (i) Using the relation for refraction at a single spherical refracting surface, derive the lens maker s formula. (ii) In Fig 17.97, the direct image formed by the lens (f=10 cm) of an object placed at O and that formed after reflection from the spherical mirror are formed at the same point O. What is the radius of curvature of the mirror? Q-76. A right-angled isosceles glass prism is made from glass of refractive index 1.5. Show that a ray of light incident normally on (i) one of the equal sides of this prism is deviated through 90 0 (ii) the hypotenuse of this prism is deviated through 180 0 Q-77. A glass slab is placed over a page in which letters are printed in different colours. Will the image of all the letters lie in the same plane? CONCEPTUAL PROBLEMS 7
Q-78. In the previous problem, which letter would appear to be maximum raised and which letter would appear to be minimum raised? Q-79. A man, wanting to obtain the picture of a zebra, photographs a while donkey after fitting a glass with black streaks on the lens of the camera. Can the man succeed in his purpose? Q-80. What are the five general features of the image formed by a plane mirror? Q-81. Our eye is sensitive to yellow colour. But red light is used for danger signals. Why? Q-82. Within a glass slab, a double convex air bubble is formed. How would the air bubble behave? Q-83. Images formed by totally reflected light are brighter than the images formed by ordinary reflected light. Why? Q-84. Light of wavelength 5000 Ǻ falls on a plane reflecting surface. What are the wavelength and frequency of reflecting light. For what angle of incidence is the reflected ray normal to the incident ray? Q-85. What is the twinkling effect of starlight due to? Q-86. Q-87. Can light travelling from air to glass suffer total internal reflection? Justify your answer. The image of an object formed by a lens on the screen is not in sharp focus. Suggest a method to get a clear focusing of the image on the screen without disturbing the positions of the object, the lens or the screen. Q-88. A beam of light of wavelength 400 nm is incident normally on a right angled prism as shown. It is observed that the light just grazes along the surface AC after falling on it. Given that the refractive index of the material of the prism varies with the wavelength λ as per the relation μ A = 1.2 + b/ λ 2. Calculate the value of b and the refractive index of the prism material for a wavelength λ = 5000 Ǻ. Q-89. A spherical surface of radius of curvature R, separates a rarer and a denser medium as shown in Fig 17.99. Complete the path of the incident ray of light, showing the formation of a real image. Hence derive 8
the relation connecting object distance u, image distance v, radius of curvature R and the refractive indices n 1 and n 2 of the two media. LONG ANSWER QUESTIONS Q-90. A lens forms a real image of an object. The distance from the object to the lens is u cm and the distance of the image from the lens is v cm. The given graph shows variation of v with u. (i) What is the nature of the lens? (ii) Using the graph, find the focal length of this lens. Q-91. Show by a diagram the image formation of a point object by a thin double convex lens having radii of curvature R 1 and R 2. Hence derive the formula 1 f = (n - 1) 1 R 1 1 R 2, where f is the focal length and n is refractive index of material of the lens. Q-92. Obtain an expression for the effective focal length of a combination of two thin lenses placed in contact coaxially with each other. Q-93. Show by drawing diagrams how a totally reflecting glass prism can be used to deviate a ray of light through (i) 90 0 (ii) 180 0 and invert it. 9
Q-94. By stating the sign conventions used and assumptions made, derive the expression : - μ 1 + μ 2 = μ 2 μ 1, u v R when the refraction takes place from rarer to denser medium at concave spherical refracting surface. Symbols used here have their usual meanings. Q-95. State new Cartesian sign conventions. Derive the expression : - μ 1 + μ 2 = μ 2 μ 1, when refraction occurs u v R from rarer to denser medium at convex spherical refracting surface (μ 1 < μ 2 ). Q-96. An equiconvex lens with radii of curvature of magnitude r each, is put over a liquid layer poured on top of a plane mirror. A small needle, with its tip on the principal axis of the lens, is moved along the axis until its inverted real image coincides with the needle itself. The distance of the needle from the lens is measured to be a. On removing the liquid layer and repeating the experiment, the distance is found to be b. Given that two values of distances measured represents the focal length values in the two cases, obtain a formula for the refractive index of the liquid. 10