Question

Using Huygens's construction, show how a plane wave is reflected from a surface. Hence verify the law of reflection.

Answer 1

Laws of reflection:

• 1^st law: It claims that the angle of incidence and angle of reflection are equal.
• 2^nd law: According to this statement, the incident ray, the reflected ray, and the incident point normal all lie in the same plane.

The first law of reflection. Let XY be a plane reflecting surface and AB be a plane wavefront incident on the surface as shown in the figure.
According to the Huygens principle, every point on wavefront AB is a source of secondary wavelet and the time during which wavelet from reaches C, the reflected wavelet from A would arrive at D.

i.e. `t = (BC)/v = (AD)/v`

or BC = AD ...............(i)

`v` = velocity of light in the medium

In a right-angled triangle ΔABC,

`sini = (BC)/(AC)`

or BC = AC sini ..............(ii)

In ΔADC

`sinr = (AD)/(AC)`

or AD = AC sinr .........(iii)

Putting equations (ii) and (iii) in (i), we get

AC sini = AC sinr

sini = sinr

or i = r

This is the first law of reflection.

In the second law of reflection, from the figure we find that the incident ray, the reflected ray and the normal all lie on the same plane XY. This proves the second law of reflection.