All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.
20. Angle to first fringe = 13.7 degrees. distance on screen = 2.4 m
22. Angle to first minimum = 0.970 degrees, width of peak = 8.46 cm
24. 2.2 cm
40. 169 nm
44. The minimum thickness for constructive interference is 113 nm. The minimum nonzero thickness for destructive interference is 225 nm.
46. When the apparatus is immersed in liquid, the wavelengths are reduced by a factor of the index of refraction. Otherwise, the analysis presented in the textbook for Newton's rings applies. Comparing the radii of the rings when immersed and not immersed, and taking a ratio gives index of refraction 1.39.
56. 61.2 degrees
58. 45 degrees
60. 60 degrees
62. For light coming from water into air, Brewster's angle is 36.9 degrees. The critical angle for total internal reflection is 48.8 degrees (remember the last course). For light coming from air into water, Brewster's angle is 53.1 degrees. The sum of the two Brewster's angles is 90 degrees.
2. Light shining on something makes it warm, so it must carry energy.
3. Light is described as rays when we are talking about how it interacts with things much larger than its wavelength. In that case, diffraction can be ignored, and the light always travels in straight lines. Light is described as waves when we talk about how it interacts with things of about the same size as a wavelength, or less. Then diffraction is important.
4. There is destructive interference if the paths differ by half a wavelength, or half a wavelength plus any number of whole wavelengths.
5. The wavelength of light is less in water, by a factor the index of refraction, which is about 1.33. The distance between fringes is proportional to the wavelength, so they would be a factor of 1.33 closer together.
6. Blue light has a shorter wavelength, so the distance between the fringes would be less than with red light.
7. I am not sure what answer is expected here. Both are interference effects which occur only for waves, not particles.
8. Except for the size of the slits needed to produce diffraction, which are much bigger for sound waves, the interference of sound and light waves through a pair of slits is very similar.
9. The sources of light must be coherent, or vibrating in phase, to produce diffraction. Headlights are not a coherent source of light.
10. The light is bent both when it enters and exits a flat window glass in opposite amounts, so that the net angle is zero. Therefore, all colors leave the glass at the same angle at which they entered.
11. Violet light is bent at a larger angle than red light, meaning that it has a shorter focal length, both for converging and diverging lenses.
12. Sound waves are much longer than light waves, and are large compared to the size of a door. Therefore, they are diffracted significantly when going through openings the size of a door. Light is not diffracted because it has a wavelength much smaller than a door.
13. Increasing the slit width decreases the size of the diffraction pattern, while increasing the wavelength increases the size of the diffraction pattern.
14. The diffraction grating will produce lines of the same separation as the two slits, but they will be much brighter and narrower, especially at large orders.
15. A diffraction grating also produces interference between lines separated by multiples of the minimum line spacing. For example, there are lines produced by interference between every other line in the grating as well. This produces a set of bright spots between the spots produced by the adjacent lines.
16. Many slits multiplies the intensity of the spots, and also makes them narrower. Closely spaced slits makes the spots spread further apart.
17. For a diffraction grating, long wavelengths are bent more, so that the top color will be violet for the grating described. Red will be bent most and appear at the bottom. For the prism in the same situation, violet light is bent most and red light the least. This is backwards from the diffraction grating, so the red line will appear on top in this case.
18. The thickness of the film must be consistent to within less than a wavelength of light. A piece of glass is much thicker than a wavelength of light, and normally not consistently thick in such a way that it would produce coherent interference.
19. Because of the curvature of the top glass, the distance between the glasses changes more rapidly at the edges than at the center, so the rings are closer together.
20. If the coated lens appears greenish-yellow, it is eliminating a complementary color, which would be blueish-purple.
21. We didn't discuss the Michelson interferometer, so you can skip this.
22. Polarization tells us that light travels as a transverse wave. Longitudinal waves such as sound cannot have polarization.
23. Light that scatters in the atmosphere, or is reflected off objects, is partially polarized. Polarizing sunglasses are therefore more effective at reducing glare.
24. If you hold a pair of polarizing glasses up to the sky and rotate it, the darkness of the sky will change. So will the brightness of light reflecting from windows and other objects.
25. If the earth had no atmosphere, the sky would be black, because no light would be scattered.
26. If the atmosphere were 50 times denser, the blue light would scatter more, as it does during a sunset. So the sky would probably appear reddish.
| Physics 222 | Department of Physics | University of Tennessee |