Explain, reflection of light on the basis of Hygen's secondary wavelet theory with suitable diagram?

Huygen's Principle:

(i) Every point on a given wave front (called primary wave front) acts as a fresh source of new disturbance, called secondary wavelets which travel in all directions with the velocity of light in the medium.

(ii) The forward envelope of these secondary wavelets gives the new wave front at any instance.This is called secondary wave front.

Imagine incoming rays are incident on a surface. Here the wavefronts are plane waves. In plane wavefront, the wavefronts will be infinite parallel planes to each other with constant amplitude. Consider the plane wave AB which falls on the reflecting surface. AB is the incident wavefront and is drawn as perpendicular to the incident ray. It falls at an angle i on the surface. Now according to the Huygens’s principle every point on AB act as a source of secondary wavelets. Consider the points A and B as new sources which emits the secondary waves. The velocity of the propagation of waves is ‘v’. Let ‘t’ be the time taken. So let’s assume that vt be the distance moved by the secondary wavelets. AA₁ and BE are the secondary waves. Now the new wavefront should be a tangents line which connects those two secondary waves. The reflected waves should be perpendicular to the new wavefront. A₁E is the new tangential line which connects the secondary wavelets.

Consider ΔABE and ΔAA₁E. Here AE is common.

1 = 90^° .

AA₁ = BE.

These triangles are congruent triangles

 So  

Thus Angle of Incidence = Angle of Reflection. This is the first law of reflection.

The incident wavefront, the reflected wavefront and normal lie in the same plane which is perpendicular to the reflecting surface. This again verifies the second law of reflection. Therefore, the two Laws of Reflection are verified using Huygens’s Principle.

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