Using Huygens principle, show that the angle of incidence is equal to angle of reflection during a plane wave front reflected by a plane surface.

Explanation

Mn `to` Reflecting plane surface (mirror)
I `to` angle of incidence
r `to` angle of reflection
v`to` speed of light wave
Let `tau` be the time taken by the wave front to travel from the point B to C, then distance BC =v`tau`
In order the construct the reflected wave front a sphere of radius =v`tau` is drawn from the point A as shown in the above figure .Let CE represent the tangent plane drawn from the point C to this sphere.Then AE=BC=v `tau` ,ABC=CEA =`90^(@)` and AC is common .
The triangle ABC and CEA are congruent .Thus i=r
Detailed Answer:
AB is the wavefront incident on a reflecting surface XY with an angle of incidence `anglei` .According to Huygen.s principle ,every point on AB acts as a source of secondary wavelets.

At first ,wave incidents at point A and then to points C,D and E
`A_(1)E` represents the tangential envelope of the secondary wavelets in forward direction
In `DeltaABE` and `DeltaAA_(1)E`
`angleABE=angleAA_(1)E=90^(@)`
Also ,side AE is common .
`AA_(1)=BE`=distance travelled by wave in same time so,these triangles are congruent.
So, `angleBAE=anglA_(1)EA`
So, `anglei=angler`
Hence.angle of incidence =angle of reflection .