Question

Explain Huygens construction of spherical wavefront.

Answer 1

Hint: According to the Huygens theory of light, the source will emit light in the form of spherical waves. Light waves spread over all directions. The disturbance from the source covers equal distance in equal time distance in all directions in spherical shape. The point on the sphere surface will receive disturbance simultaneously. All points on this surface are in the same phase. Such a surface is called the equiphase surface. Part of the equiphase surface is called a wavefront.

Complete step by step solution:
First, let’s understand what a waveform is?
Wavefront is the locus of all the points which receive the light disturbance simultaneously from a source and therefore vibrate in the same phase. A part of this surface is called a wavefront. It is geometrical construction to determine the new position of a wavefront at any later instant from its position at any earlier instant. Spherical wavefront is formed when the point of observation is very close to the primary source. Consider a point source ‘S’ placed in a homogeneous medium which emits light waves in all directions. Let A, B, C, D and E be points on the spherical wavefront formed at any instant t. From Huygens’s principle, every point on this wavefront adds a secondary source of light emitting secondary waves. The secondary wavefront is represented by a circle with equal radius and centres of point A, B, C, D and E. Let c be the velocity of light in an isotropic homogeneous medium.
The envelope or tangential surface P’Q’ gives a new spherical wavefront after time t.
In time t secondary waves cover distance ‘ct’. Taking A, B, C, D & E and ‘c.t’ as a radius draws hemispheres. Tangential envelope of all these hemispheres gives a new wavefront at t. This surface is passing through A’, B’, C’, D’ AND E’. This surface is the new wavefront at that instant’.

Note: There are three kinds of wavefront: spherical, plane, cylindrical. Before Huygens theory, there are various theories about the nature of light such as Newton’s corpuscular theory. He said that every source of light emits a minute, tiny particle known as corpuscles in a medium surrounding the source. To explain to Huygens principle, he explains two terms: wave surface, wavefront, wave normal. Wave normal is a straight line drawn perpendicular to the wavefront at any point on the wavefront at any instant and pointing in the direction of propagation of the light is called wavefront.