Question

Explain refraction of light on the basis of wave theory. Hence prove the laws of refraction

Answer 1

Laws of refraction :
The ratio of the velocity of light in rarer medium to the velocity of light in a denser medium is a constant called the refractive index of denser medium w.r.t. rarer medium. The incident rays, refracted rays, and normal lie in the same plane. Incident ray and refracted ray lie on opposite sides of normal.

Explanation :
Phenomenon of refraction can be explained on the basis of wave theory of light.

1. Let XY be the plane refracting surface separating two media air and glass of respectively. indices μ₁ and μ₂ refractive.
2. A plane wave front AB is advancing obliquely towards XY from the air. It is bounded by rays AA₁ and BB₁ which are incident rays.
3. When ‘A’ reaches ‘A₁’, then ‘B’ will be at ‘P’. It still has to cover distance PB1 to reach XY.
4. According to Huygens’ principle, secondary wavelets will originate from A₁ and will spread over a hemisphere in the glass.
5. All the rays between AA₁ and BB₁ will reach XY and spread over the hemispheres of increasing radii in the glass. The surface of the tangency of all such hemispheres is RB₁.
   This gives rise to refracted wavefront B₁R in the glass.
6. A₁R and B₁R₁ are refracted rays.
7. Let c1 and c₂ be the velocities of light in air and glass respectively.
8. At any instant of time ‘t’, distance covered by incident wavefront from P to B₁ = PB₁ = c₁t Distance covered by a secondary wave from A₁ to R = A₁R = c₂t.