Question

Show that angle of incidence is equal to angle of reflection and also they lie in the same plane.

Or

Using Huygens’ principle, derive laws of reflection.

Answer 1

Let XY be a plane reflecting surface and AB be a plane wavefront incident on the surface as shown in Fig.

According to Huygens’ principle, every point on wavefront AB is a source of secondary wavelets and the time during which wavelet from B reaches at C, the reflected wavelet from A would arrive at D.

If t is the time taken by wavelet from B to C [or A to D] then

t = \(\frac{BC}{v} = \frac{AD}{v}\) ............(i)

First law of reflection.

Putting Eq. (ii) and (iii) in Eq. (i), we get

AC sin i = AC sin r

or sin i = sin r

or i = r

i.e. Angle of incidence = Angle of reflection.

This proves first law of reflection.

Second law of reflection

Since incident ray, reflected ray and the normal all lie on the same plane i.e. plane XY, so second law of reflection is also proved.