Proof for Laws of Reflection at a Plane Surface (By Huygens' Wave Theory)

Chapter-10|Wave Optics|NCERT 12th Physics:

Proof for laws of Reflection at a Plane Surface (By Huygens' Wave theory):

When parallel rays comes from infinity at any instant a ray touches point A and at that time another ray touches point B, At that time first wavefront AB will be formed and it will be perpendicular to incident ray and let time is zero.

Let after t time, second ray covers a distance vt and reaches at point C. At point C we will form a wavelet. Now taking A as centre we will form an arc with radius vt(point D) and here we will make another wavelet. Now we will draw a common tangent from C to D, which will be make second wavefront(reflected wave front). Now we will draw perpendicular lines to this wavefront and it will be reflected rays.

Further, the incident wavefront AB, the reflecting surface AC and the reflected wavefront CD are perpendicular to the plane of the paper.

Also incident rays are perpendicular to AB, normal is perpendicular to AC and reflected rays are perpendicular to CD.

Therefore, incident ray, normal and reflected ray all lies in the same plane.

This is second law of reflection.