Question

Write Huygens principle of light wave. Prove the laws of reflection or refraction of light on the basis of Huygens principle of light.

Answer 1

Reflection of Light - Consider a reflecting surface XY on which a plane wavefront AB is incident at A. According to Hyygens's principle each point on the wavefront AB acts as a source of new disturbance. By the time secondary wave-let from B reaches C on the reflecting surface.The ceondary waves let from A travels a distance AD =BC. Taking A as the centre and radius = AD or BC, draw a sphere.

Now join tangent to the sphere at D with Point C.

CD is the reflected plane wavefront. Time taken by wavelets to reach from B to C or from A to D is given by

where v is speed or light BC = AD.........(i)

The wavefront CD will be the reflected wavefront if the secondary wavelets from all the points on the incident wavefront take the same time to reach the reflectred wavefront CD. Let a secondary wavelet starts from point p on the incident wavefront and reaches the point R on the wavefront CD after reflecting from the surface XY at point Q then the time taken by this secondary wavelet is given by

Since the different secondary wavelets arising from the incicent wavefront fall of different points like Q on the  reflecting surface XY, so the values of AQ for different secondary wavelets are different  As all the secondary wavelets take the same time to go from the incident wavefront to the reflected happen only if co-efficient of AQ in eqn. (v) is zero

i.e. sini = sinr

or,i = r proved.

Refraction of Light:

Let XY  be a plane surface separating two media and let PA be a plane wavefront just incident on it. Normals LA and MP to the incident wavefront represent incident rays.AN is normal to the  surface at the point A. ∠NAL = i the angle of incidence. 

The wavefront first strikes at A, so secondary wavelets will start first from A. which travel with velocity C₂  in the second medium .During time t, the disturbance teaches from p to p'. In this the secondary wavelet from A will travel a distance C₂ t  in the second  medium with A as centre and C₂ t radius, we draw an are and from p', we draw a tangent P 'A' .P 'A' is the refracted wavefront,(Fig)

Consider a ray QKQ' such that QK is perpendicular to AP and KQ' is perpendicular to A'P'. The time taken by the ray to travel a distance QK + KQ' is

The rays from different points on the incident wavefront will take the same time to reach the corresponding points on the refracted wavefront. It is possibly only if t,is independent of AK.

¹μ₂, is called the refractive index of second medium with respect to the first medium and the above equation is called Snell's law.