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# Wave Front, Huygens’ Wave Theory

Introduction
The branch of optics in which we study about the nature of light, its production, emission and propagation is called Physical optics and this also the wave nature of light. This branch mainly deals about the different properties of light like reflection, refraction, interference, diffraction and polarization.
Wave-front
According to the wave theory of light, when light from a source travels into the medium, it produces the disturbance on the particles of the medium. But, in the homogeneous medium, the disturbance received by the particles at any time at the same distance from the source is exactly same and the variation on the particles of the mediums are in same phase with each other. If we join the vibration which are in phase we get a path. These path is called wave-front. Also, every points of the wave-fronts act as a source and the Huygen's principle is based on this assumption. The points of a wave-front acts as s new source are called wavelets.
OR, it is the locus of particle which are at equidistance from the source and vibrating in same phase. Wavefronts can be explained only in the medium based type of a sources. It is basicallly divided into three categories. They are:

(i) Spherical wave front

(ii) Cylinddrical wave front

(iii) Plane wave front

Huygen's Wave Theory
It explain the propagation of light energy in medium. In other words, it gives the position of secondary wave front. It explained the propagation of ligt energy by considering following point which is called Huygen's principle.
Each point of primary wave front can be taken as source of new disturbance. The disturbance produced from the each point is called secondary wave front. The speed of wavelet is same with the speed of light. The figure illustrarion of Huygen's principle is as shown in the diagram below.

In the figure, AB is the primary wavefront , the position of the partilce in the wave front is denoted by a, b ,c and so on. Each point acts as source for new disturbance. The sphere with radius (T) is known as wavelets. The position of secondary wavefront can be obtained by constructing an outward tangential plane to all wavefronts.

(i) According to this theory, velocity of light is greater in rearer medium than in denser medium.

(ii) These theory explains the phenomena like reflection, refraction, interference, diffraction successively.

(i) These theory is silent about the backward envelope.

(ii) According to these theory, light is longitudinal wave but it was cleared that, light is transverse wave after the invention of polarization.

Application Of Huygen's Principle

(1) Law of reflection

Consider a reflecting surface xy in which plane wavefron AB is incident with an angle of (i) which is equal to angle of incident.
Let 1, 2 anad 3 are the direction of incident rays then the reflected rays from the reflecting suface xy are along the direction of 1', 2' and 3'. According to Huygen's prnciple, each point of wavefront AB' can be taken as source for new disturbance. Let the disturbance produced by the particle at position B' is A', so that B'A' = c.t $\dotsm$ (1)
At the same time the disturbance produced by the particle at point A is at B so that AB = c.t $\dotsm$(2)
Again, from Huygens principle , the position of secondary wavefront can be obtained by constructing the tangentail palne to all wavelets. In figure above, BA' refer to position of secondary wavefront. Now, from the triangle ABA' and AB'A'.
(i) $\angle$ABA' = $\angle$AB'A' = 90$^\circ$ [Angel between incident rays and corresponding wavefront is always 90$^\circ$. ]
(ii) AB = BA' = c.t
(iii) AA' = A' A [ concurrent triangle, the corresponding angle remain same. ]
Further more the incident wavefront, reflected wavefront and the normal lies in a plane.
Therefore, incident ray reflected ray and normal all lies at a point plane of paper.

(ii) Law of refraction

Consider a refracting surface xy in which a plane wave front, AB is incident with angle i which is equal to the angle of incident. Let 1, 2, and 3 be the direction of the incident rays . According to Huygens principle each point of the wave front AB can be taken as source for new disturbance. Let the disturbance produced by the particle at position B to A' so that BA' = ct
Same instant of time the disturbance produced by the particle at point A to B' so that AB' = vt $\dotsm$ (ii)
(where v be the speed of light I medium.)
Again, from the Huygens's principle, the position of secondary wave front can be obtained by constructing the tangential plane to all wavelets, in the figure A'B' refers to position of secondary wave front which is also called wave reflected wave front. Let us consider r be the angle of reflection.
Now from the triangle ABA',
Sin i = $\frac{BA'}{AA'}$ = $\frac{ct}{AA'}$
And from triangle AA'B',
Sin r = $\frac{AB'}{AA'}$ = $\frac{vt}{AA'}$
Therefore, $\frac{sin i}{sin r}$ = $\frac{c}{v}$ = $\mu$ which proved.
Furthermore, the incident wave front, refracted wave front and normal all lies at a point in a plane of paper.