Verify the laws of reflection using Huygen's wave principle.

Explanation

Consider a plane wave front AB incident on the plane mirror `M_(1)M_(2)`. The figure shows angle of incidence `=anglei=angleBA A.`. Also lines 1, 2, 3 are the incident rays perpendicular to wave front AB. Now, according to Huygen.s principle, every point on the wave front AB is the sorce of secondary wavelets.

Let the secondary wavelets from point B reach point A. in time .t. then BA. = c. t ...(i)
Where c is the velocity of light. Suppose secondary wavelets from a point A reach point B. in time t, then AB. = c. t ...(ii)
From equations (i) and (ii) BA.=AB. ...(iii)
Join A.B.. Then A.B. is the reflected wave front and 1., 2., 3. are the reflected rays perpendicular to A.B.. Also `angleB.A.A=angler`= angle of reflection
From similar triangle AA.B and AA.B., we have
BA. = AB. = c.t. [from equation (iii)]
`angleB=angleB.` [Both are `90^(@)`]
AA. = AA. [base common]
Hence, triangles are congruent.
`rArranglei=angler` This is the Snell.s law of reflection.