# Laws of Refraction on the Basis of Huygens’s Wave Theory

Let us consider a plane wavefront AB incident on surface PQ. Let v_{1} and v_{2} be the velocity of incident and reflected ray respectively such that (v_{1} > v_{2}). At first, the wavefront A hits the surface PQ and then C reaches and hits at the last. Now, from Huygens’s principle, A and C in turn becomes a source of secondary spherical wavelets. Let ‘t’ be the time taken by the disturbance at B to reach C.

∴ BC = v_{1}t……(i)

During this time, the secondary wavelet created at A has travelled a distance AD = v_{2}t in the medium (ii). With A as centre and AD as a radius, a circle is drawn. This circle represents secondary spherical wavefront at a time t, that has emerged from A. Thus the envelope to wavelets is refracted wavefront CFD.

Now, in Δ ABC, $\text{sini} = \frac{ \text{BC}}{\text{AC}}$

In Δ ACD, $\text{sinr} = \frac{ \text{AD}}{\text{AC}}$

$\text{ or,} \frac{ \text{sini}}{\text{sinr}} = \frac{ \text{BC/AC}}{\text{AD/AC}} = \frac{ \text{BC}}{\text{AD}}$

$\text{ or,} \frac{ \text{sini}}{\text{sinr}} =\frac{ \text{v}_1t}{\text{v}_2t} $

\text{ or,} \frac{\text{sini}}{\text{sinr}} =\frac{\text{v}_1}{\text{v}_2} = \mu$

This is the ratio of sine of the angle of incidence to the sine of the angle of refraction. It is constant for the given pair of media. So, snell’s law is proved.

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## 4 Responses to “Laws of Refraction on the Basis of Huygens’s Wave Theory”

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