Question

Explain dependence of wavelength on the refractive index of the medium

Answer 1

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When a light ray goes from one medium to another its frequency remain invariable. The velocity changes from medium to medium and hence wavelength to the proportion of velocity also changes since the frequency is constant.

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Answer 2

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Refractive Index:-

The refractive index n is the factor by which a wave slows down relative to the speed of light in vacuum c0 . The speed of a wave v is

v=c0n

In vacuum, n=1.0 and the speed is c0 . Speed v , frequency f , and wavelength λ are related through

v=fλ

In a vacuum, this equation is

c0=fλ0

where λ0 is called the free space wavelength. When a wave enters a second medium, its speed and wavelength change, but the frequency remains constant. This may be a weird concept so here is a link to an animation of a wave going from vacuum into second medium where the speed and wavelength slow down but frequency remains constant.

Reflection Coefficient:-

Perhaps you meant reflection coefficient r . The reflection coefficient quantifies the amplitude of a reflected wave relative to the incident wave.

r=ErefEinc

The equations for calculating the reflection coefficient are called the Fresnel equations and they are a bit complicated. Here is a link to a one-page summary of scattering at an interface and the Fresnel equations are given.