Reflection of wave

 Reflection of  a light wave on a plane surface

To understand reflection of light on a plane surface in form of wave, let us consider wavefront AB incident on a plane surface  making an angle 'i' with surface as shown in below figure.

In this figure, when wavenormal A is at point D, then wave B reaches at point O.As the both wave is in same medium their velocity is same. Let the velocity of wave is 'v' . After incident on the surface at D the wave startt forming next waveform in the same medium  in forward direction and reaches point F in time 't' covering a distance DF= 'vt' and on the same time the wave at point O moves in forward direction and reaches point C covering a distance of  OC = 'vt' in time 't' .

As wave travel in same medium thus distance covered by wave is given by DF = OC = vt.

Now according to huygens principle , the common tangent FC gives the next wave and thus reflection takes place. 

Now In triangle DFC and Triangle DOC,

 DC = DC --------------( Common side)

 DF = OC  ( Distance tarvelled in same time)

Angle  DFC = Angle DOC --------( each 90)

thus Triangle DFC ∽ Triangle DOC 

 Angle ODC = Angle OCD -------(corresponding angle)

Angle i = Angle r 

When reflection take place Angle i = Angle r

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