Prove laws of reflection using Huygens' principal.
(OR) Proof for laws of reflection using Huygens' Principal:

Explanation

Let us consider a parallel beam of light, incident on a reflection plane surface such as a plane mirror XY. The incident wavefront is AB and the reflected wavefront is A.B. in the same medium. These wavefront are perpedicular to the incident rays L,M and reflected rays L.. M. respectively. By the time point A of the incident wavefront touches the reflecting surface, the point B is yet to travel a distance BB. to touch the reflecting surface a B..
When the point B falls on the reflecting surface at B.. the point A would have reached A.. This is applicable to all the points on the wavefront. Thus, the reflected wavefront A,B. emanates as a plane wavefront. The tow normals N and N. are considered at the points where the rays L and M fall on the reflecting surface.
As reflection happens n in the same medium, the speed of the light is same before and after the reflection. Hence, the time taken for the ray to travel from B to B. is the same as the time taken for the ray to travel from A to A. . Thus, the distance BB. is equal to the distance AA.: (AA. = BB.),

(i) The incident rays, the reflected raya and the normal are in the same plane.
(ii) Angle of incidence,
`angle i = angle NAL = 90^(@) - angle NAB = angle BAB.`
Angle of reflection,
`angle r = angle N.B.M. = 90^(@) - angle N.B.A = angle A.B.A`
For the two right angle triangles, `Delta ABB. and Delta B.A.A` the right angles, `angle B and angle A`. are equal `(.angle B and angle A. = 90^(@))`, the two sides, AA. and BB. are equal, (AA. = BB.), the side AB. is the common. Thus, the two triangles are congurent, As per the property of congruency, the tow angles, `angle BAB. and angle A.B.A` must also be equal.
i = r
Hence, the laws of reflection are proved.