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The wavelength of a monochromatic light in vacuum is λ. It travels from vacuum to a medium of absolute refractive index μ. The ratio of the wavelength of the incident wave to that of the refracted wave is ______.

Asked in GUJCET 2007 · Snell's law, slabs and apparent depth

• (1) μ² : 1
• (2) 1 : 1
• (3) μ : 1
• (4) 1 : μ

Step-by-step solution

Why the other options are wrong

• (1) Only one factor of μ enters. The speed falls to c/μ and the frequency is unchanged, so λₘ=λ/μ; a ratio μ²:1 would need the speed to fall by μ².
• (2) It is the frequency that is unchanged on refraction, not the wavelength. The wave slows down in the medium, so its wavelength must shorten with it.
• (4) This is the ratio written the other way round. The refracted wave is the shorter one, λ/μ, so incident : refracted =μ:1.

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