State Hugen's principle and verify the laws of reflection of light using this principle.

Explanation

Law of Reflection on the basis of Huygens principal : Consider plane wavefront AB incident on a plane reflection surface `M_(1)M_(2)` as shown in Fig. At first the wavefront touches the reflection surface at B followed by the successive points towards C. `angle ABC` = i, the angle of incidence. According to Huygens principle, the secondary wavelents starts growing from each point on BC with speed C. When the secondary wavelets from A touch the poing C, the secondary wavelets from A touch the point C, the secondary wavelets from B spread over semi-sphere of radius `C xx t`, where C is speed of light and t is time taken by the wavelenght to travel from to A toC. The tangent plane CD is the new reflected wavefront and `angle DCO = r`, the angle of reflection.
Time taken by light to to from P to Q is given by
` t=(PO)/(C)+(OQ)/(C)=(BOsini)/(C)+(OCsinr)/(C)`
In `Delta POB`,
`(PO)/(BO)=sini`
In `Delta QOC`
`(OQ)/(OC)=sinr`
OQ = OC sin r
`t=(BOsini)/(C)+((BC-BO)sinr)/(C)`
`t=(BCsinr)/(C)+(BO(sinr-sinr))/(C)`
Different rays from the wavefront AB have different values of BO. for CD to be the true reflected wavefront, the above time must be independent of BO.
`therefore sin i - sin r = 0`
or `sin i = sin r` Angle of incident = Angle of reflection
which is the first law of reflection.
Also, the incident ray SB, the normal BN and relfeted ray BD all lie in the same plane, i.e, in the plane of papaer. This is the second law of reflection. Hence, the laws of reflection are proved.