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Unformatted text preview: Light and Optical Fibers for the Internet 439 Consider in more detail what happens when light encounters the electrons in the atoms making up the very fi rst layer of the medium’s surface. When the light hits those electrons, oscillating electric and magnetic forces are exerted on them. As a result, the electrons begin oscillating at the same frequency at which the light wave oscillates. We know from Chapter 7 that an oscillating electron will emit light. These electrons, which are oscillating as a consequence of light striking them, emit some light of their own. This emitted light has the same frequency as the electron’s oscillation, which is the same as the frequency of the incident light. This emitted light travels in the same direction as the incident light and adds to the original wave. From this, we conclude: The frequency of a light wave is unchanged when it enters a transparent medium, although the speed of the wave changes. Let us see what this fact implies about the light’s wavelength. Recall that the wave- length equals the distance the wave travels in one period T (one full oscillation cycle). Let us introduce the symbol λ n for the wavelength in the medium. The equation relat- ing wavelength to speed and period is: wavelength = speed multiplied by time between peaks , or λ n = c n ⋅ T The fact that the frequency remains unchanged when the wave enters the medium implies that the period also remains unchanged (because f = 1/ T ). The equation λ n = c n ⋅ T implies that the wavelength must change if the speed changes. The wavelength becomes shorter in a dense medium than it was in the surrounding vacuum (or air). This is because in a fi xed time interval the wave travels a shorter distance in the medium than it would in vacuum. We conclude that the wavelength inside a medium equals the wave- length in vacuum divided by n . That is, The wavelength of light inside a medium with refractive index equal to n is: λ λ n n = We illustrate this behavior by drawing waves inside and outside of the medium, as in Figure 13.3 . Here we consider a medium for which n = 2. The wave arrives from the left, travels to the right, and enters the medium. The wave speed slows for the light inside of the medium, then speeds up again when the wave exits the medium. Remember that the frequency is the same everywhere. From the relation c n = c / n , we deduce that the speed inside the medium is one-half of the speed outside. In this case, the wavelength inside is one-half as long as the wavelength outside. As the wave moves from left to right, a crest outside of the medium travels a distance λ in the same time ( T ) that a crest on the inside travels a distance λ /2....
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