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37 - Interference of Light Waves

# 37 - Interference of Light Waves - Chapter 37 Interference...

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Chapter 37 Interference of Light Waves CHAPTER OUTLINE 37.1 Conditions for Interference 37.2 Young’s Double-Slit Experiment 37.3 Intensity Distribution of the Double-Slit Interference Pattern 37.4 Phasor Addition of Waves 37.5 Change of Phase Due to Reﬂection 37.6 Interference in Thin Films 37.7 The Michelson Interferometer 1176 ± The colors in many of a hummingbird’s feathers are not due to pigment. The iridescence that makes the brilliant colors that often appear on the throat and belly is due to an interference effect caused by structures in the feathers. The colors will vary with the viewing angle. (RO-MA/Index Stock Imagery)

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1177 I n the preceding chapter, we used light rays to examine what happens when light passes through a lens or reﬂects from a mirror. This discussion completed our study of geometric optics . Here in Chapter 37 and in the next chapter, we are concerned with wave optics or physical optics, the study of interference, diffraction, and polarization of light. These phenomena cannot be adequately explained with the ray optics used in Chapters 35 and 36. We now learn how treating light as waves rather than as rays leads to a satisfying description of such phenomena. 37.1 Conditions for Interference In Chapter 18, we found that the superposition of two mechanical waves can be constructive or destructive. In constructive interference, the amplitude of the resultant wave at a given position or time is greater than that of either individual wave, whereas in destructive interference, the resultant amplitude is less than that of either individual wave. Light waves also interfere with each other. Fundamentally, all interference associ- ated with light waves arises when the electromagnetic ﬁelds that constitute the individ- ual waves combine. If two lightbulbs are placed side by side, no interference effects are observed because the light waves from one bulb are emitted independently of those from the other bulb. The emissions from the two lightbulbs do not maintain a constant phase relationship with each other over time. Light waves from an ordinary source such as a lightbulb undergo random phase changes in time intervals less than a nanosecond. Therefore, the conditions for constructive interference, destructive interference, or some intermediate state are maintained only for such short time intervals. Because the eye cannot follow such rapid changes, no interference effects are observed. Such light sources are said to be incoherent. In order to observe interference in light waves, the following conditions must be met: The sources must be coherent —that is, they must maintain a constant phase with respect to each other. The sources should be monochromatic —that is, of a single wavelength. As an example, single-frequency sound waves emitted by two side-by-side loudspeak- ers driven by a single ampliﬁer can interfere with each other because the two speakers are coherent—that is, they respond to the ampliﬁer in the same way at the same time.
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37 - Interference of Light Waves - Chapter 37 Interference...

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