WEBVTT
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This is College Physics
Answers with Shaun Dychko.
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We're going to show that when a light
ray travels from air into water,
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its wavelength changes such that it becomes
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0.75 times in the water
when it was in the air.
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So, the speed of wave in a medium
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is its frequency times its
wavelength in that medium
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and this is the speed in a vacuum
divided by the index of refraction.
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And basically, index of refraction is
defined this way, and that it's *C* over *V*.
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And, you can see that by
showing how these are related.
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In which case, *V* equals *C* over *N*.
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And, this is the wave equation
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that the speed of a wave equals its
frequency times its wavelength.
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So, we can solve this for the wavelength
in a medium of some index of refraction *N*,
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that's why the subscript N is there
by dividing both sides by frequency.
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And, we get the wavelength in a medium
is the speed of light in a vacuum
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divided by frequency times the
index of refraction of the medium.
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So, to answer this question, we
take the wavelength in water
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and divide it by the wavelength in air.
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And then, we substitute this
formula in place of each *Lambda*.
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So, we have speed of light
divided by frequency
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times index of refraction of the water.
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This replaces *Lambda* and *W*.
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And then, we're going to divide
by the wavelength in air,
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but I'm going to instead multiply
by the reciprocal of this,
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because it gets messy when you
divide a fraction by a fraction.
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So, we're going to multiply by the
reciprocal of the wavelength in air.
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So, that's frequency times
index of refraction of air
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divided by speed on light in a vacuum.
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Notice that the frequency does not
get a subscript water and air
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because the frequency doesn't change.
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It's only the wavelength that changes.
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So, the *C*'s and the *F*'s cancel,
and the ratio of wavelengths
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is the reciprocal of the ratio
of the indexes of refraction.
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So, the wavelength in water
divided by the wavelength in air
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is the index of refraction of air divided
by the index of refraction of water.
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So, that's one divided by 1.33, which is 0.75.