Question

Using Huygens’ principle, verify the laws of reflection at a plane surface.

Answer 1

Verification of Laws of Reflection using Huygens Principle

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 the velocity of light, then the 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 (1),

`t = (AK sin i)/c + (KP'sin r)/c`

`t = (AK sin i + (AP' - AK)sin r)/c`  (∵ KP' = AP' - AK)

`t = (AP' sin r + AK(sin i - sin r))/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.