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When a light wave passes from one medium to other, the wavelength of the light wave changes and the frequency remains constant. If then color of the light waves depends on changing wavelength or Frequency?

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Frequency ($\nu$) stays constant since it is a characteristic property of the source. Using the relation $v = \lambda \nu$ in the definition of the refractive index, $n = c/v$, your required answer follows.

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