Question

Consider a point source emitting waves uniformly in all directions.

1. Draw two wave fronts very near to the point source.

2. Using Huygen’s principle, prove that angle of incidence is equal to angle of reflection.

3. What is the shape of a plane wave front after passing through a thin convex lens?

Answer 1

1.

2.

AB is the incident wavefront and CD is the reflected wavefront, ‘i’ is the angle of incidence and r’ is the angle of reflection. Let c₁ be the velocity of light in the medium. Let PO be the incident ray and OQ be the reflected ray.

The time taken for the ray to travel from P to Q is

O is an arbitrary point. Hence AO is a variable. But the time to travel for a wave front from AB to CD is a constant. So eq.(2) should be independent of AO. i.e., the term containing AO in eq.(2) should be zero.

∴ \(\frac{AO}{C_1}\)(sin i - sin r) = 0

sin i – sin r = 0

sin i – sin r

i = r 

This is the law of reflection.

3. Spherical wave front.