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


Let us consider a plane wavefront AB incident on surface PQ. Let v1 and v2 be the velocity of incident and reflected ray respectively such that (v1 > v2). 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 = v1t……(i)

During this time, the secondary wavelet created at A has travelled a distance AD = v2t 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.

Do you like this article ? If yes then like otherwise dislike : 9

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

  1. rajnish

    it was awesome………….
    this site is really good…..

  2. ALISH KHADGI

    dherai thau khojira hey simple and easy answer ko lagi finally afnai daju vai ko website kam lago
    thankyou soooo much

  3. tannu

    law of refraction of light on the basis of huygens wave theory explain in easy method

  4. N.RAMASWAMY

    YOUR LECTURES ARE SIMLY SUPERB – NO ONE CAN MATCH YOUR PRESENTATION. EXCELLENT MATERIAL FOR THE STUDENTS.
    I AM A RETIRED PROFESSOR OF MECH. ENGG. AND I REALLY ENJOYED YOUR LECTURE.

    MAY YOUR ORGANISATION CONTINUE TO DO THIS FANTASTIC JOB OF EDUCATING OUR YOUNG BOYS AND GIRLS AND MAKE THEM USEFUL CITIZENS OF THIS GREAT COUNTRY
    RAMASWAMY.N (022-21639556)