Einstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,

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1 1 O P T I C S 1. Define resolving power of a telescope & microscope and give the expression for its resolving power. 2. Explain briefly the formation of mirage in deserts. 3. The radii of curvature of a double convex lens are 15 cm and 30 cm and its refractive index is 1.5. Calculate the focal length of the lens. 4. What do you understand by polarisation of light? How can the transverse nature of light be demonstrated experimentally? 5. (a) Draw a labelled diagram of a compound microscope and explain its working. With the help of ray diagram, illustrate the formation of the final image of an object in a compound microscope. Derive an expression for its magnifying power. How can the magnifying power be increased? How will the resolving power of compound microscope be affected when (a) the frequency of light used to illuminate the object is increased, and the focal length of the objective is increased. Justify your answer in each case. 6. (a) Give a relation between path difference and wave length for constructive and destructive interference between two waves. Define phase difference and relate this with the path difference. 7. Two lenses, one converging of power 8 Dioptres and the other diverging of power 4 Dioptres, are combined together. Calculate the focal length and power of the combination. 8. Define circulary polarised light & plane polarised light. 9. What is the magnifying power of a telescope whose objective and eyepiece have focal lengths 180 cm and 3 cm respectively? 10. Two lenses, one diverging of power 2 Dioptres and the other converging of power 6 Dioptres, are combined together. Calculate the focal length and power of the combination. 11. (a) State Huygen s Wave theory and its assumptions? Also define coherent source of light Deduce laws of reflection laws of refraction on the basis of Huygen s principle. 12. (a) Draw a labelled ray diagram of an astronomical telescope and explain its working. (d) Draw a labelled diagram of an astronomical telescope forming the final image at the near point. Write down the formula for its magnifying power. What is the effect of increasing the diameter of the objective of a telescope on its magnifying power and resolving power? Draw a labelled ray diagram for a refracting type astronomical telescope. How will its magnifying power be affected on increasing for its eye-piece the focal length, and the aperture? Justify your answer. 13. (a) Do the frequency and wavelength change when light passes from a rarer to a denser medium? Light of wavelength 6000 Å in air enters a medium of refractive index 1.5. What will be its frequency in the medium?

2 2 14. (a) A slit of width a is illuminated by monochromatic light at normal incidence. Draw the intensity distribution curve observed on the screen, due to diffraction. Determine the angular separation between central maximum and first order maximum of the diffraction pattern due to a single slit of width 0.25 mm. when light of wavelength 5890 Å is incident on it normally. In a single slit diffraction pattern, how is the angular width of central bright maximum changed, when the slit width is decreased the distance between the slit and the screen is increased 15. An object is placed at 0.06 m from a convex lens of focal length 0.10 m. Calculate the position of the image. 16. (a) What is total internal reflection? Under what conditions does it take place? Derive the relation between refractive index of a medium and its critical angle. A ray of light while travelling from a denser to a rarer medium undergoes total internal reflection. Derive the expression for the critical angle in terms of the speed of light in the respective media. 17. Find the ratio of intensities at two points x and y on a screen in Young s double slit experiment, where waves from S 1 and S 2 have path difference of 0 and / Show, by drawing ray diagrams, how a totally reflecting glass prism can be used to deviate a ray of light through For the same angle of incidence, the angles of refraction in three different media A, B and C are 15 0, 25 0 and 35 0 respectively. In which medium will the velocity of light be minimum? 20. Give two difference between interference and diffraction pattern of light. 21. Calculate the refractive index of the material of an equilateral prism for which the angle of minimum deviation is Two coherent sources whose intensity ratio is 81 produce interference fringes. Calculate the ratio of intensity maxima and minima in the fringes system. 23. A concave mirror and a concave lens are held in water. What changes, if any, do you expect in their respective focal length as compared to their values in air. 24. You are given two convex lenses of focal length 80 mm and 800 mm. Which one will you use as an objective and which one as an eyepiece for constructing an astronomical telescope? Trace the course of rays through the two lenses to show the formation of final image of a distant object. Derive an expression for the magnifying power of the telescope for normal adjustment. 25. The two slits in Young s double sit experiment are separated by a distance of 0.03 mm. An interference pattern is produced on a screen 1.5 m away. The 4th bright fringe is at a distance of 1 cm from the central maximum. Calculate the wavelength of light used. 26. Explain why white light is dispersed when passing through a prism. 27. Give two differences between fringes formed in single slit diffraction and Young s double sit experiment. 28. Deduce lens maker s formula for a thin biconves lens. 29. How can one distinguish between an unpolarized light beam and a linearly polarized light beam using a polaroid? 30. The radius of curvature of each face of biconcave lens, made of glass of refractive 1.5 is 30 cm. Calculate the focal length of the lens in air.

3 31. An astronomical telescope consists of two thin lenses set 36 cm apart and has a magnifying power 8. Calculate the focal lengths of the lenses. 32. Why is difraction of sound waves easier to observed than diffraction of light waves? What two main changes in diffraction pattern of a single slit will you observe when the monochromatic source of light is replaced by a source of white light? 33. Give reasons for following observations on the surface of moon : (iii) Sun-rise and sun-set are abrupt Sky appears dark A rainbow is never observed. 34. What changes in interference pattern will be observed when the monochromatic source of light is replaced by source of white light? 35. Give the ratio of velocities of light rays of wavelengths 4000 Å and 8000 Å vacuum. 36. Refractive index of glass for lights of yellow, green and red colours are µ y, µ g and µ r respectively. Rearrange these symbols in an increasing order of values. 37. Derive the expression for the fringe width in Young s double slit interference experiment. 38. At what angle of incidence should a light beam strike a glass slab of refractive index 3, such that the reflected and the refracted rays are perpendicular to each other? 39. A glass prism of refracting angle 60 0 and refractive index 1.5, is completely immersed in water of refractive index Calculate the angle of minimum deviation of the prism in this situation. (sin = ) 40. A double convex lens made of glass of refractive index 1.5 has both radii of curvature of magnitude 20 cm. An object 2 cm high is placed at 10 cm from the lens. Find the position, nature and size of the image. 41. A double concave lens made of glass of refractive index 1.5 has both radii of curvature of magnitude 40 cm. An object 2 cm high is placed at 10 cm from the lens. Find the position, nature and size of the image. 42. The image of an object formed by a lens on the screen is not in sharp focus. Suggest a method to get clear focusing of the image on the screen without disturbing the position of the object, the lens or the screen. 43. Sketch the wave-fronts corresponding to converging rays. 44. Draw a labelled ray diagram to show the image formation in a reflecting type telescope. Write its two advantages over a refracting type telescope. On what factor does its resolving power depend? 45. Draw a ray diagram to show formation of image by a refracting type astronomical telescope. On what factors does its magnifying power and resolving power depend? 46. How does the magnifying power and resolving power of a telescope change on increasing the diameter of its objective? Give reasons for your answer. 47. What are coherent source of light? Why is no interence pattern observed when two coherent sources are infinitely close to each other? far apart from each other? 48. A slit of width d is illuminated by light of wavelength 6,500 Å. For what values of d will the first minimum fall at an angle of diffraction of 30 0? first maximum fall at an angle of diffraction of 30 0? 3

4 4 49. Draw a ray diagram to show the formation of the image of an object placed between f and 2f of a thin concave lens. Deduce relation between the object distance, the image distance and the focal length of the lens under this condition. 50. How does the resolving power of a compound microscope change on decreasing the wavelength of light used, and decreasing the diameter of its objective lens? 51. Draw a ray diagram to show the formation of the image of an object placed between the optical centre and focus of a convex lens. Deduce the relationship between the object distance, image distance and focal length under the conditions stated. 52. A concave lens is placed in water. Will there be any change in focal length? Give reason. 53. A thin symmetric double convex lens of power P is cut into three parts A, B & C. What will be the power of the portion A and B. 54. Define power of a lens. Write its S.I. unit. 55. What should be the position of an object relative to a biconvex lens so that it behaves like a magnifying lens? 56. How are resolving power and limit of resolution of an optical instrument related? 57. How does the focal length of a convex lens change if monochromatic blue light is used instead of monochromatic red light? 58. For which of the following cases : sin i sin r µ µ What is the focal length and power of the lens in the figure. The radii of curvature of the two faces are R each.

5 60. What is the maximum and minimum magnification of the microscope? 61. What is a wavefront? 62. What is the phase difference between two points on a wave front? 63. A small piece of stone is dropped into a still water reservoir. What is the shape of wave front formed? 64. A light wave enters from air to glass. How will following be affected : Energy of the wave? Frequency of the wave? 65. Why does a soap bubble appear dark just before brusting? 66. Give the names of two phenomenons which establish the wave nature of light. 67. What should be the order of size of obstacle or aperature for the light to diffract. 68. A ray of light falls on a transparent slab of µ = 3. If reflected and refracted rays are mutually perpendicular, find out the angle of incidence? 69. A polariser and an analyzer are so oriented that no light is transmitted. The analyzer is then rotated through What fraction of the maximum light is transmitted? 70. Write any two uses of polaroid. 71. Two polaroids are placed at 90 0 to each other and its transmitted intensity is zero. What happens when one more polaroid is placed between these two, bisecting the angle between them? Why does a pencil placed vertically looks shorter when placed in a liquid of higher refractive index? 73. Define lateral displacement. On what factor does it depend? 74. When two prisms of crown and flint glass are placed inverted to each other and in contact. What will be the effect on the emerging light? 75. A glass have a refractive index of 1.5. A convex lens made of thin glass has a focal length of 20cm in air. It is in water whose refractive index is 4/3 immersed. Calculate the apparent change in focal length of the lens. 76. Complete it with correct value of angle of emergence. 77. You are given two symmetrical convex lens of focal length 20cm & 10 cm. Which of them would you prefer to use as a magnifying glass and why?

6 6 78. Draw two more rays of light from the object which form the image. 79. Why cannot we obtain interference using two independent source of light? 80. Law of energy conservation is obeyed in interference pattern. Justify. 81. In young s double slit experiment. How is the fringe width changes when Light of smaller frequency is used. Distance between the slit is increased. 82. State the necessary conditions for sustained interference. 83. A double convex lens of focal length is broken into two equal halves at the axis. Then two halves are combined as shown in fig. What is the focal length of the combination. 84. What is Dispersion? Define dispersive power. 85. Define angular dispersion and dispersion power. How are these two related? 86. Draw ray diagram through an equilateral prism showing the conditions for minimum angle of A m Sin 2 deviation and hence prove that : µ. SinA / 2 µ 1 a 87. State the principle of reversibility of light and hence prove that g. µ g a 88. A convex lens made of material of refractive index µ 1 is immersed in a fluid of refractive index µ 2. Trace the path of parallel beam of light passing through the lenses when µ 1 = µ 2 µ 1 < µ 2 (iii) µ 1 > µ Explain why the sky appears blue and the sun appears red at sunset? 90. A ray of light passes through an equilateral prism in such a manner that the angle of incidence is equal to angle of emergent and each of these angle is equal to 3/4 of the angle of the prism. Find angle of deviation. 91. Two convex lens of same focal length but their aperature 5 cm and 10 cm are used as object lens in two astronomical telescopes.

7 (a) What will be the ratio of their Resolving Power Magnifying Power Compare the intensity of images formed in these cases. 92. A ray of light is incident at an angle of 60 0 on first face of prism of angle 30 0 the ray emerging out of prism make an angle 30 0 with incident ray. Show that emergent ray is perpendicular to the face through which it emerges. Also claculate the refractive index of material of the prism. 93. Define interference of light. Two sources of equal amplitude are used to produce interference. Drive an expression for the variation of intensity with phase angle. Hence plot a graph to show this variation. Also derive an expression for the variation of intensity with phase angle for unequal amplitude. 94. Use the lens equation to deduce algebrically, that (a) An object placed within the focus of a convex lens produces a virtual and enlarged image. A concave lens produce a virtual and diminshed image independent of the location of the object. 95. Draw a ray diagram to show the formula of real images of a point object due to convex spherical refracting surface, when the ray of light is travelling from rarer medium of Refractive index (µ 1 ), to denser media of Refractive Index (µ 2 ). Using the diagram derive a relation between object distance (u) and image distance (v) radius of curvature R of a convex spherical surface. State the sign conventions and the assumptions made. 96. What is Polarization? State Brewster s Law and hence deduce the expression for polarising angle. 97. In given figure, F 1 and F 2 are focal points of the lens placed in air. When an object is placed at o, its image is formed at l. Calculate its focal length A fish is situated at the depth h inside a lake. Calculate the radius of circular aperture through which the fish seen the out wide world. 99. A reflecting telescope has a large mirror for its objective with radius of curvature equal to 80 cm. What is the magnifying power of the telescope if the eyepiece used has a focal length of 1.6 cm? 100. Draw the ray diagram to show how right angle isosceles prism can be used to : deviate the ray through 180 0? deviate the ray through 90 0? (iii) invert the ray?

UNIT-5 EM WAVES UNIT-6 RAY OPTICS

UNIT-5 EM WAVES UNIT-6 RAY OPTICS UNIT-5 EM WAVES 2 Marks Question 1. To which regions of electromagnetic spectrum do the following wavelengths belong: (a) 250 nm (b) 1500 nm 2. State any one property which is common to all electromagnetic