What is the relationship between lamda and refractive index?
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The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, and similarly the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
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Therefore, we can conclude that the wavelength is inversely proportional to the refractive index of the material in which the wave is travelling.
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