On the basis of Huygen.s wave theory, show that when light is incident on a plane mirror obliquely, angle of reflection is equal to angle of incidence.

Explanation

Consider a plane wavefront AB incident on a reflecting surface SS..

According to Huygen.s principle, each point on the wavefront acts as a new source of secondary wavelets. So wave takes time 1 second to move from wavefront AB to BA
i.e., AB. = BA. = vt
where, v is the velocity of wave.
From triangles ABA and A.B.A
`angleB=angleB.=90^(@)`
AA.=A.A= common
AB.=A.B=vt
Therefore, the two triangles are congruent
`:. angle B A A.= angleB.A.A`
or `anglei=angler`
This is the second law of reflection.
Since AB, A.B. and SS. are in the plane of the paper, they will also be in the same plane. Therefore, the incidence ray, the reflected ray and the normal at the point of incidence are all in the same plane. This is the first law of reflection.
Hence, the laws of reflection are proved by Huygen.s principle.