Wavefront and Huygens Principle of Wave Propagation


Wavefront

A wavefront is defined as the continuous locus of all the particles which are vibrating in the same phase. The perpendicular line drawn at any point on the wavefront represents the direction of propagation of the wave at that point and is called the ‘ray’.

Types of Wavefronts : The wavefronts can be of different shapes. In general we experience two types of wavefronts.

(i) Spherical Wavefront : If the waves in a medium are originating from a point source, then they propagate in all directions. If we draw a spherical surface centred at point-source, then all the particles of the medium lying on that spherical surface will be in the same phase, because the disturbance starting from the source will reach all these points simultaneously. Hence in this case the wavefront will be spherical and the rays will be the radial lines [Fig (a)].

(ii) Cylindrical Wavefront : If the waves in a medium are originating from a line source, then they too propagate in all directions. In this case the locus of particles vibrating in the same phase will be a cylindrical surface. Hence in this case the wavefront will be cylindrical. (Fig b)

(iii) Plane Wavefront : At large distance from the source, the radii of spherical or cylindrical wavefront will be too large and a small part of the wavefront will appear to be plane. At infinite distance from the source, the wavefronts are always plane and the rays are parallel straight lines.

The equation represents the plane wave propagating along positive direction of X-axis.

Huygens’ Principle of Wave Propagation

This principle is useful for determining the position of a given wavefront at any time in the future if we know its present position. The principle may be stated in three parts as follows :

(i) Every point on a given wave-front may be regarded as a source of new disturbance.

(ii) The new disturbances from each point spread out in all directions with the velocity of light and are called the secondary wavelets.

(iii) The surface of tangency to the secondary wavelets in forward direction at any instant gives the new position of the wave-front at that time.