Chapter 33: Interference and Diffraction

1. Chapter 33: Interferenceand Diffraction Section 33-1: Phase Difference and Coherence

2. A phase shift of 180º occurs when a light wave • is transmitted through a boundary surface into a medium that is more dense than the medium from which the wave came. • is transmitted through a boundary surface into a medium that is less dense than the medium from which the wave came. • reflects from the boundary surface of a medium that is less dense than the medium in which the wave is traveling. • reflects from the boundary surface of a medium that is more dense than the medium in which the wave is traveling. • Both c and d are correct.

3. A phase shift of 180º occurs when a light wave • is transmitted through a boundary surface into a medium that is more dense than the medium from which the wave came. • is transmitted through a boundary surface into a medium that is less dense than the medium from which the wave came. • reflects from the boundary surface of a medium that is less dense than the medium in which the wave is traveling. • reflects from the boundary surface of a medium that is more dense than the medium in which the wave is traveling. • Both c and d are correct.

4. Which, if any, of the following conditions is not necessary for the light waves from two sources to be coherent? • They must have the same frequency. • They must have the same amplitude. • They must have the same wavelength. • They must have a constant phase difference. • All of these conditions are necessary.

5. Which, if any, of the following conditions is not necessary for the light waves from two sources to be coherent? • They must have the same frequency. • They must have the same amplitude. • They must have the same wavelength. • They must have a constant phase difference. • All of these conditions are necessary.

6. Diffraction of sound waves is more readily observable than that of light waves because • sound waves are longitudinal and not transverse. • sound waves have a higher frequency than light waves. • sound waves have a lower velocity than light waves. • sound waves have longer wavelengths than do light waves. • sound waves occur in air and light waves do not.

7. Diffraction of sound waves is more readily observable than that of light waves because • sound waves are longitudinal and not transverse. • sound waves have a higher frequency than light waves. • sound waves have a lower velocity than light waves. • sound waves have longer wavelengths than do light waves. • sound waves occur in air and light waves do not.

8. In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. The container is surrounded by air. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is • 1 only • 2 only • 3 only • 1 and 2 • 2 and 3

9. In the figure, a beam of light from an underwater source is incident on a layer of carbon disulfide and the glass bottom of the container. The container is surrounded by air. Some of the refracted and reflected rays are shown in the diagram. For the rays shown, the interface at which the reflected light changes phase is • 1 only • 2 only • 3 only • 1 and 2 • 2 and 3

10. The two waves shown come from a source where they were initially coherent. The path difference could be • ⅓ λ • ½ λ • ¼ λ • λ • It is not possible to answer this question without additional information.

11. The two waves shown come from a source where they were initially coherent. The path difference could be • ⅓ λ • ½ λ • ¼ λ • λ • It is not possible to answer this question without additional information.

12. The phase difference for the two waves shown in the figure is • 2π • π • 2π/3 • π/2 • It is not possible to answer this question without additional information.

13. The phase difference for the two waves shown in the figure is • 2π • π • 2π/3 • π/2 • It is not possible to answer this question without additional information.

14. Which of the following statements is true? • When two harmonic waves of the same frequency and wavelength but differing in phase combine, the resultant wave is a harmonic wave whose amplitude depends on the phase difference. • A phase difference between two waves can be the result of a difference in path length. • A path difference of one wavelength is equivalent to no phase difference at all. • A phase difference between two waves can be the result of reflection from a boundary surface. • All of these are correct.

15. Which of the following statements is true? • When two harmonic waves of the same frequency and wavelength but differing in phase combine, the resultant wave is a harmonic wave whose amplitude depends on the phase difference. • A phase difference between two waves can be the result of a difference in path length. • A path difference of one wavelength is equivalent to no phase difference at all. • A phase difference between two waves can be the result of reflection from a boundary surface. • All of these are correct.

16. Chapter 33: Interferenceand Diffraction Section 33-2: Interference in Thin Films

17. For us to see interference phenomena in a thin film, • the incoming light must be monochromatic. • the index of refraction of the thin film must be greater than the index of refraction of the material below it. • the index of refraction of the thin film must be less than the index of refraction of the material below it. • the incoming light must be multicolored. • None of these conditions need exist.

18. For us to see interference phenomena in a thin film, • the incoming light must be monochromatic. • the index of refraction of the thin film must be greater than the index of refraction of the material below it. • the index of refraction of the thin film must be less than the index of refraction of the material below it. • the incoming light must be multicolored. • None of these conditions need exist.

19. Why are fringes not observed if the angle of the wedge of air in the diagram is too large? • For a large angle, the small-angle approximation (sin θ≈θ) is not valid. • The light passing through the wedge of air loses its coherence. • The fringes overlap. • The fringes are too close together to be seen individually. • None of these is correct.

20. Why are fringes not observed if the angle of the wedge of air in the diagram is too large? • For a large angle, the small-angle approximation (sin θ≈θ) is not valid. • The light passing through the wedge of air loses its coherence. • The fringes overlap. • The fringes are too close together to be seen individually. • None of these is correct.

21. For two identical rays of light to interfere destructively, their path lengths • must be equal. • must differ by an odd number of half wavelengths. • must differ by an integral number of wavelengths.

22. For two identical rays of light to interfere destructively, their path lengths • must be equal. • must differ by an odd number of half wavelengths. • must differ by an integral number of wavelengths.

23. The main effect contributing to the production of different colors seen on a soap bubble is • the dispersion of light by the water in the soap. • the interference of light reflected from the front and back of the soap film. • the polarization of light by the soap film. • total internal reflection of light in the soap film. • None of the statements is correct.

24. The main effect contributing to the production of different colors seen on a soap bubble is • the dispersion of light by the water in the soap. • the interference of light reflected from the front and back of the soap film. • the polarization of light by the soap film. • total internal reflection of light in the soap film. • None of the statements is correct.

25. A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately • 7.1 m • 7.4 m • 6.5 m • 6.8 m • 7.8 m

26. A wedge-shaped film of air is formed by placing two flat glass plates with one end touching each other and the other end spaced by a gold leaf. The wedge is then illuminated using a monochromatic light of wavelength 590 nm from above and the complete fringe pattern is shown. The thickness of the gold leaf is approximately • 7.1 m • 7.4 m • 6.5 m • 6.8 m • 7.8 m

27. A wedge-shaped film of air is formed by placing a glass plate of unknown flatness upon second glass plate that is known to be perfectly flat. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. The wedge of air is thicker on the right than on the left. From the fringe pattern one can conclude that the bottom surface of the first glass plate is • perfectly flat. • concave. • convex. • No conclusion can be drawn about the shape.

28. A wedge-shaped film of air is formed by placing a glass plate of unknown flatness upon second glass plate that is known to be perfectly flat. The wedge is then illuminated using a monochromatic light from above and a fringe pattern is shown. The wedge of air is thicker on the right than on the left. From the fringe pattern one can conclude that the bottom surface of the first glass plate is • perfectly flat. • concave. • convex. • No conclusion can be drawn about the shape.

29. The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens • is more curved on the left and right sides compared to top and bottom. • is more curved on the top and bottom compared to the left and right sides. • has a spherical surface. • has a concave surface. • None of the above statements is correct.

30. The interference pattern is from a lens placed on a flat reflecting surface illuminate using a monochromatic light from above. From the pattern one can conclude that the lens • is more curved on the left and right sides compared to top and bottom. • is more curved on the top and bottom compared to the left and right sides. • has a spherical surface. • has a concave surface. • None of the above statements is correct.

31. Chapter 33: Interferenceand Diffraction Section 33-3: Two-Slit Interference Pattern and Concept Check 33-1

32. Two narrow slits are illuminated by monochromatic light. If the distance between the slits is equal to 2.75 wavelengths, what is the maximum number of dark fringes that can be seen on a screen? • 2 • 3 • 4 • 5 • 6

33. Two narrow slits are illuminated by monochromatic light. If the distance between the slits is equal to 2.75 wavelengths, what is the maximum number of dark fringes that can be seen on a screen? • 2 • 3 • 4 • 5 • 6

34. Which of the following statements about Young's double-slit experiment is false? • The bands of light are caused by the interference of the light coming from the two slits. • The results of the double-slit experiment support the particle theory of light. • Double-slit interference patterns can also be produced with sound and water waves. • If the slits are moved closer together, the bands of light on the screen are spread farther apart. • The pattern of light on the screen consists of many bands, not just two bands.

35. Which of the following statements about Young's double-slit experiment is false? • The bands of light are caused by the interference of the light coming from the two slits. • The results of the double-slit experiment support the particle theory of light. • Double-slit interference patterns can also be produced with sound and water waves. • If the slits are moved closer together, the bands of light on the screen are spread farther apart. • The pattern of light on the screen consists of many bands, not just two bands.

36. The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern • increases by a factor of 2. • increases by a factor of 4. • depends on the width of the slits. • decreases by a factor of 2. • decreases by a factor of 4.

37. The distance between the slits in a double-slit experiment is increased by a factor of 4. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes near the center of the interference pattern • increases by a factor of 2. • increases by a factor of 4. • depends on the width of the slits. • decreases by a factor of 2. • decreases by a factor of 4.

38. In a double-slit experiment, the distance from the slits to the screen is decreased by a factor of 2. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes • increases by a factor of 2. • increases by a factor of 4. • depends on the width of the slits. • decreases by a factor of 2. • decreases by a factor of 4.

39. In a double-slit experiment, the distance from the slits to the screen is decreased by a factor of 2. If the distance between the fringes is small compared with the distance from the slits to the screen, the distance between adjacent fringes • increases by a factor of 2. • increases by a factor of 4. • depends on the width of the slits. • decreases by a factor of 2. • decreases by a factor of 4.

40. In order to produce several easily visible interference fringes from two narrow slits using light of a single wavelength, the distance between the slits must be of the order • of a few tenths of the wavelength. • of a few wavelengths. • of a few tens wavelengths. • of a few hundreds wavelengths. • The distance does not matter.

41. In order to produce several easily visible interference fringes from two narrow slits using light of a single wavelength, the distance between the slits must be of the order • of a few tenths of the wavelength. • of a few wavelengths. • of a few tens wavelengths. • of a few hundreds wavelengths. • The distance does not matter.

42. When the slits in Young’s experiment are moved closer together, the fringes • remains unchanged. • move closer together. • move further apart.

43. When the slits in Young’s experiment are moved closer together, the fringes • remains unchanged. • move closer together. • move further apart.

44. A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line? • 1.0 mm • 2.0 mm • 3.0 mm • 4.0 mm • 1.2 mm

45. A narrow, horizontal slit is 0.50 mm above a horizontal plane mirror. The slit is illuminated by light of wavelength 400 nm. The interference pattern is viewed on a screen 10.0 m from the slit. What is the vertical distance from the mirror to the first bright line? • 1.0 mm • 2.0 mm • 3.0 mm • 4.0 mm • 1.2 mm

46. Chapter 33: Interferenceand Diffraction Section 33-4: Diffraction Pattern of a Single Slit

47. When a parallel beam of light is diffracted at a single slit, • the narrower the slit, the narrower the central diffraction maximum. • the narrower the slit, the wider the central diffraction maximum. • the width of the central diffraction maximum is independent of the width of the slit.

48. When a parallel beam of light is diffracted at a single slit, • the narrower the slit, the narrower the central diffraction maximum. • the narrower the slit, the wider the central diffraction maximum. • the width of the central diffraction maximum is independent of the width of the slit.

49. The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. Which graph represents the diffraction pattern from the widest single slit?

50. The graphs are plots of relative intensities of various diffraction patterns versus the sine of the angle from the central maximum. Which graph represents the diffraction pattern from the widest single slit?