Change in velocity of light with change in optical density

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hey guys! we know that velocity of a wave = wavelength x frequency. and speed of light changes with change in optical density. so there must be change in either frequency or wavelength or both. which of these quantities change with change in optical density? and why?
 

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Andy Resnick
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The wavelength changes by l' =l/n, where n is the (real part of the) index of refraction. The wavelength changes instead of the frequency because the momentum is given by wavelength, while energy is given by frequency.
 

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