Question

Explain Huygen's principle of secondary wavelets.

Answer 1

Huygen's principle of secondary wavelets: In order to explain the propagation of waves in medium Huygen propounded a principle known as Huygens principle of secondary wavelets. It made the three following assumptions:
(i) When a disturbance is caused in a medium, the particles of the medium start vibrating. The surface in the medium, on which each particle vibrates in same phase, is called the wave front. In a homogeneous medium, the wave front is normal to the direction of propagation of the wave. If the source is like a point at a finite distance, the wave front is always spherical. If the source is very far (i.e. at infinite distance) the wave front is plane. If the source is in form of a slit at a finite distance, the wave front is cylindrical.
(ii) Every point of the medium on a given wave front is a centre of originating new disturbance. This new disturbance is called the secondary wavelet. If the medium is homogeneous, the secondary wavelets travel with the same speed as the speed with which the original wave front travels.
(iii) The common tangential surface (or envelope) drawn on these secondary wavelets at any instant, represents the position of new wave front at that instant.
For example in Fig. (a) let $AB$ be the position of spherical wave front at any instant originated from a point source $S$. According to Huygen's principle, secondary wavelets are given out from each particle of medium on this wave front $AB$, which travel forward with the speed $v$ of the original wave front. Hence to obtain the position of new wave front after time $t$, draw spheres of radius $vt$ with such point $a$, $b$, $c$, $d$..... of the wave front $AB$ as centre. The common envelope of all these spheres is $A_1{B}_1$ which represents the position of new wave front after a time $t$. It may be mentioned here that the wave front $AB$, not only produces the wave front $A_1{B}_1$ forward moving, but it will also produce a wave front $A^{{}^{\prime }}{B}^{{}^{\prime }}$ moving backwards. Huygen could not successfully explain the absence of the backward wave front $A^{{}^{\prime }}{B}^{{}^{\prime }}$.
In the same manner, the forward movement of plane wave front is explained in Fig.