Use Huygens' principle to verify the laws of refraction.

#### Solution

Huygens' Principle to Verify the Laws of Refraction :

Consider any point Q on the incident wavefront PA.

When the disturbance from P on incident wavefront reaches point P', the disturbance from point Q reaches Q'.

If c is velocity of light, then time taken by light to go from point Q to Q'(via point K) is given by,

`t=(QK)/c+(KQ')/c`....(i)

In right-angled ΔAQK,

∠QAK = i

∴ QK = AK sin i

In right-angled ΔKQ'P'

∠Q'P'K=r

∴ KQ'=KP'sin r

Substituting these values in equation (i),

`t=(AKsini)/c+(KP'sinr)/c`

`t=(AKsini+KP'sinr)/c`

`t=(AKsini+(AP'-AK)sinr)/c` [∵ KP'=AP'-AK]

`t=(AP'sinr+AK(sini-sinr))/c` .....(ii)

The rays from different points on incident wavefront will take the same time to reach the corresponding points on the reflected wavefront, if ‘*t*’ given by equation (ii) is independent of AK.

∴ AK (sin i − sin r) = 0

sin i − sin r = 0

sin i = sin r

i = r

i.e., the angle of incidence is equal to the angle of reflection.

Also, the incident ray (LA or MP'), reflected ray (AA'L' or P'M'), and the normal (AN) − all lie in the same plane.