HUYGENS PRINCIPLE AND INTERFERENCE

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1 HUYGENS PRINCIPLE AND INTERFERENCE VERY SHORT ANSWER QUESTIONS Q-1. Can we perform Double slit experiment with ultraviolet light? Q-2. If no particular colour of light or wavelength is specified, then the refractive index of the medium refers to which colour? Q-3. Name one effect which could not explained by Huygens wave theory. Q-4. What is the effect on fringe width if the distance between the coherent sources is decreased? Q-5. Why a thin film of oil on the surface of water appears coloured? Q-6. Can we produce interference with white light? Q-7. In Young s double slit experiment, a thin plate of some transparent material is introduced in the path of one of the interfering rays. What would happen? Q-8. What will be the effect on the interference pattern if the phase difference between the two interfering waves changes continuously? Q-9. Can you produce interference with sound waves in air? It should be noted here that sound waves are longitudinal. Q-10. Can we produce interference with two electric bulbs placed side by side? Q-11. Q-12. Name any five factors on which the speed of light in vacuum depends. Does the speed of light in vacuum depend upon (i) direction of propagation (ii) wavelength (iii) intensity of wave? Q-13. A region is illuminated by two sources of light. The intensity I at each point is found to be equal to I 1 + I 2 where I 1 is the intensity of light at the point when source 2 is absent. I 2 is similarly defined. Are the source coherent or incoherent? Q-14. Does the speed of light in vacuum depend upon the nature of source? Q-15. Is the speed of light in glass independent of the colour of light? 1

2 Q-16. When light travels from a rarer to a denser medium, it loses some speed. Does the reduction in speed imply a reduction in the energy carried by the light wave? Q-17. In the wave picture of light, intensity of light is determined by the square of the amplitude of the wave. What determines the intensity of light in the photon picture of light? Q-18. What is the effect on the interference pattern in Young s double slit experiment when : screen is moved closer to the plane of slits? Explain your answer in each case. Q-19. Two slits in Young s double slit experiment are illuminated by two different sodium lamps emitting light of same wavelength. No interference pattern will be obtained. Is this statement true or false? Q-20. Why the central fringe in Lloyd s mirror experiment is dark and not bright? Q-21. How does the central fringe appear when white light is used in a biprism experiment? Q-22. What is the relation of a wavefront with a ray of light? Q-23. What happens when a thin transparent film is placed just in front of one of the two slits in the young s double slit experiment? Q-24. Define the term coherence for light waves. Q-25. What is the shape of the wavefront of a beam of parallel rays? Q-26. What is a ray of light? Q-27. What is the geometrical shape of the wavefront of the light diverging from a point source? Q-28. What will be the effect on the fringes of Young s double slit experimental set-up if immersed in water? Q-29. Q-30. Name the shape of a wavefront originating from a point source. The monochromatic source of light in Young s double slit experiment is replaced by another monochromatic source of shorter wavelength. What will be the effect? Q-31. Draw the graph showing the variation of intensity in the interference pattern in Young s double slit experiment. Q-32. What is the shape of the wavefront emitted by a light source in the form of a narrow slit? Q-33. State the path difference between two waves for destructive interference. 2

3 Q-34. State the path difference between two waves for constructive interference in terms of λ. Q-35. Two slits in Young s double slit experiment are illuminated by two different sodium lamps emitting light of the same wavelength. Will you observe the interference pattern? Justify your answer. Q-36. What is the effect on the interference fringes in Young s double slit experiment if the separation between the two slits is increased? Q-37. What is the phase difference between any two points of a wavefront? Q-38. What is the phase difference corresponding to a path difference of λ? Q-39. What is the main condition to produce interference of light? Q-40. Why bubbles of colourless soap solution appear coloured in sunlight? Q-41. Define wavefront. Q-42. What is interference of light? Q-43. State two conditions to obtain sustained interference. Q-44. What are coherent sources of light? Q-45. Give an example of interference of light in everyday life. SHORT ANSWER QUESTIONS Q-46. In a certain region in a thin film, we get 10 fringes with light of wavelength 4358 Ǻ. How many fringes will be observed in the same region with light of wavelength 5893 Ǻ? Q-47. What is the origin of fringes in Lloyd s mirror experiment? Q-48. Name six properties of light which could be explained by Huygens wave theory. Q-49. How can you justify the rejection of backward wavefront? Q-50. Does the speed of light in a medium depend upon the nature of the source? Q-51. Mercury green light has a wavelength cm. Deduce (i) frequency in MHz (ii) period (in micro second). Q-52. In Young s double slit experiment performed with a source of white light, only black and white fringes are observed. Is this statement true? 3

4 Q-53. An excessively thin film appears black in reflected light. Why? Q-54. Why should we have narrow sources to produce good interference fringes? Q-55. Oil floating on water looks coloured due to interference of light. What should be the approximate thickness of the film for such effects to be visible? Q-56. What is the shape of the wavefront originating from (i) a point source and (ii) a line source? Q-57. No interference pattern is detected when two coherent sources are infinitely close to each other. Why? Q-58. What changes in interference pattern in Young s double slit experiment will be observed when (i) distance between the slits is reduced (ii) the apparatus is immersed in water? Q-59. Q-60. Sketch the wavefront corresponding to divergent rays. Draw the type of wavefront that corresponds to a beam of white light coming from a very far off source. Q-61. Why is the interference pattern not detected when the two coherent sources are far apart? Q-62. In Young s experiment on interference, what shall happen if monochromatic source is replaced by a source of white light? Q-63. What is 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 (i) 0 and (ii) λ? Assume that the amplitudes of the waves 4 from the two sources are equal. Q-64. If the screen is moved away from the plane of the slits, then what is the effect on the interference fringes in Young s double slit experiment? Q-65. In Young s double-slit experiment. Explain with reason how the interference pattern changes, when width of the slits is increased. Q-66. How does the width of interference fringes in Young s double slit experiment change when (a) the distance between the slit and the screen is decreased? (b) frequency of the source is increased? Justify your answer in each case. Q-67. State two conditions for two light sources to be coherent. 4

5 Q-68. How would the angular separation of interference fringes in young s double slit experiment change when the distance of separation between the slits and the screen is doubled? SHORT ANSWER QUESTIONS Q-69. If a particle is thrown horizontally at a speed of m s -1 deduce the vertical fall in travelling 1 km distance. Given : g = 10 m s -1.Does that result depend upon the mass of the particle? Comment on your result, considering that Newton thought light is made up of corpuscles shot at a very large speed by the source. Q-70. Explain how Newton s corpuscular theory predicts the speed of light in a medium, say water, to be greater that the speed of light in vacuum. Is the prediction confirmed by experimental determination of the speed of light in water? If not, which alternative picture of light is consistent with experiment? Q-71. Fig shows two flat glass plates P 1 and P 2 placed nearly (but not exactly) parallel forming an air wedge. The plates are illuminated normally by monochromatic light and viewed from above. Light waves reflected from the upper and lower surfaces of the air wedge give rise to an interference pattern. (a) Show that the separation between two successive bright (or dark) fringes is given by λl 2s, where l is the length of each plate and s is the separation between the plates at the open end of the wedge. (b) In the experiment, a dark fringe is observed along the line joining the two plates. Why? (c) If the space between the glass plates in filled with water, what changes in the fringe pattern do you expect to see, if at all? experiment. (d) Suggest a way of obtaining a bright fringe along the line of contact of the two plates in this 5

6 Q-72. Fig shows an outline of Lloyd s mirror experiment. M is a plane mirror ; S is a narrow slit illuminated by some source of light (not shown) and S is the image of S in M. M, S and S are in a plane perpendicular to the paper. O represents the line of intersection of the mirror and the screen. (a) What is the origin of fringes observed on the screen? (b) Why is the slit S placed so as to have very oblique angle of incidence of light striking the mirror? (c) The two path lengths PS and PS are equal when P coincides with O. Yet the fringe at O is found in the experiment to be dark and not bright. What does this observation imply? Q-73. Answer the following questions : (a) In a thin-film interference experiment (the experiment on Newton s rings), the central fringe of the pattern is dark when viewed by reflected light, bright when viewed by transmitted light. Why? (b) If white light is used in the air wedge interference experiment or the Newton s rings experiment, the colour observed in the reflected light is complimentary to that observed in the light transmitted through the same point. Why? 6

7 Q-74. What is the effect on the interference fringes in a Young s double slit experiment when the widths of two slits are increased? Q-75. Fig shows an experimental set-up similar to Young s double slit experiment to observe interference of light. Here, SS 2 SS 1 = λ 4 write the condition of (i) constructive (ii) destructive interference at any point P in terms of path difference = S 2 P - S 1 P. Does the central fringe observed in the above set-up lie above or below O? Give reason in support of your answer. Q-76. Give the shape of interference fringes observed (a) in a Young s double-slit experiment (b) In the air wedge experiment, (c) in the Lloyd s mirror experiment, (d) when a small lamp is placed before a thin mica sheet and light waves reflected from the front and back surfaces of the sheet combine to produce interference pattern on a screen behind the lamp. (Pohl s experiment), (e) from a thin air film formed by placing a convex lens on top of a flat glass plate (Newton s arrangement). Q-77. In Young s double-slit experiment, what is the effect of the following operations on interference fringes? (i) The screen is moved away from the plane of the slits. (ii) The monochromatic source is replaced by another monochromatic source of shorter wavelength. (iii) The monochromatic source is replaced by a source of white light. (iv) The width of the source slit is made wider. (v) The separation between the two slits is increased. (vi) The distance between the source slit and the plane of the slits is increased. (vii) The width of each of the two slits is of the order of wavelength of light source. 7

8 Q-78. In a double slit interference experiment, the two coherent beams have slightly different intensities I and I + I ( I << II). Show that the resultant intensity at the maxima is nearly 4I while that at the minima is nearly (δi) 2 4I. CONCEPTUAL PROBLEMS Q-79. Q-80. Bring out the essential difference between source of light and source of radio waves. What is the effect on the interference fringes in a Young s double slit experiment when the source slit is moved closer to the double-slit plane? Q-81. What is the effect on the interference fringes in a Young s double slit experiment when the width of the source slit is increased? Q-82. Sodium light has two wavelengths λ 1 = 589 nm and λ 2 = nm. As the path difference increases, when is the visibility of the fringes a minimum? Q-83. When monochromatic light is incident on a surface separating two media, both the reflected and refracted light have the same frequency as the incident frequency. Why? Q-84. A narrow pulse of light is sent through a medium. Will you expect the pulse to retain its shape as it travels through the medium? Q-85. What is the effect of slit width and wavelength of light source on fringe width of the fringes formed by Young s double slit experiment? LONG ANSWER QUESTIONS Q-86. In Young s double slit experiment, deduce the conditions for (i) constructive and (ii) destructive interference at a point on the screen. Draw a graph showing variation of the resultant intensity in the interference pattern against position x on the screen. Q-87. How is a wavefront different from a ray? Draw the geometrical shape of the wavefront when (i) light diverges from a point source and (ii) light emerges out of a convex lens when a point source is placed at its focus. 8

9 Q-88. Using Huygens principle, explain the refraction of a plane wavefront at a plane surface. Hence prove Snell s law. Q-89. What is interference of light? Prove that law of conservation of energy is obeyed during interference of light. Q-90. Derive an expression for fringe width using Young s double slit method for interference of light. What will happen, if the distance between the two slits becomes nearly zero? Q-91. Q-92. State Huygens law and derive Snell s law on its basis. Derive a mathematical expression for the width of interference fringes obtained in Young s double slit experiment with the help of a suitable diagram. Q-93. State Huygens principle. Using the geometrical construction of secondary wavelets, explain the refraction of a plane wavefront incident at a plane surface. Hence verify Snell s law of refraction. Illustrate with the help of diagrams the action of (i) convex lens and (ii) concave mirror on a plane wavefront incident on it. Q-94. Q-95. State Huygens principle for propagation of light and prove the laws of refractions on its basis. Describe Young double slit experiment and obtain an expression for the width of the fringes formed. State the factors on which the fringe width depends. Q-96. What are coherent sources of light? Why are coherent sources required to obtain sustained interference pattern? Q-97. State the principle which helps us to determine the shape of the wavefront at a later time from its given shape at any time. Apply this principle to (i) show that a spherical/plane wavefront continues to propagate forward as a spherical/plane wavefront. (ii) derive Snell s law of refraction by drawing the refracted wavefront corresponding to a plane wavefront incident on the boundary separating a rarer medium from a denser medium. Q-98. What is a wavefront? Distinguish between a plane wavefront and a spherical wavefront. Explain with the help of a diagram, the refraction of a plane wavefront at a plane surface using Huygens construction. 9

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