Page 1222 - College Physics For AP Courses

1210 Chapter 27 | Wave Optics
Analyze Data
A double slit experiment is performed using three lasers. The table below shows the locations of the bright fringes that are recorded (in meters) on a screen.
Table 27.1
Fringe
Location for Laser 1 Location for Laser 2
Location for Laser 3
3 0.371 0.344 0.395
2 0.314 0.296 0.330
1 0.257 0.248 0.265
0 0.200 0.200 0.200
-1 0.143 0.152 0.135
-2 0.086 0.104 0.070
-3 0.029 0.056 0.005
a. Assuming the screen is 2.00 m away from the slits, find the angles for the first, second, and third bright fringes for each laser.
b. If the distance between the slits is 0.02 mm, calculate the wavelengths of the three lasers used in the experiment.
c. If the amplitudes of the three lasers are in the ratio 1:2:3, find the ratio of intensities of the central bright fringes formed by the three lasers.
27.4 Multiple Slit Diffraction
Learning Objectives
By the end of this section, you will be able to:
• Discuss the pattern obtained from diffraction grating.
• Explain diffraction grating effects.
The information presented in this section supports the following AP® learning objectives and science practices:
• 6.C.3.1 The student is able to qualitatively apply the wave model to quantities that describe the generation of interference patterns to make predictions about interference patterns that form when waves pass through a set of openings whose spacing and widths are small, but larger than the wavelength. (S.P. 1.4, 6.4)
An interesting thing happens if you pass light through a large number of evenly spaced parallel slits, called a diffraction grating. An interference pattern is created that is very similar to the one formed by a double slit (see Figure 27.16). A diffraction grating can be manufactured by scratching glass with a sharp tool in a number of precisely positioned parallel lines, with the untouched regions acting like slits. These can be photographically mass produced rather cheaply. Diffraction gratings work both for transmission of light, as in Figure 27.16, and for reflection of light, as on butterfly wings and the Australian opal in Figure 27.17 or the CD pictured in the opening photograph of this chapter, Figure 27.1. In addition to their use as novelty items, diffraction gratings are commonly used for spectroscopic dispersion and analysis of light. What makes them particularly useful is the fact that they form a sharper pattern than double slits do. That is, their bright regions are narrower and brighter, while their dark regions are darker. Figure 27.18 shows idealized graphs demonstrating the sharper pattern. Natural diffraction gratings occur in the feathers of certain birds. Tiny, finger-like structures in regular patterns act as reflection gratings, producing constructive interference that gives the feathers colors not solely due to their pigmentation. This is called iridescence.
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