Law’s of reflection (on the basis of Huygen’s principle)

let AB=> plane wave front incident on a plane mirror M₁M₂

According to Huygen’s principle, each point on the incident wave front act as a new source of light and emit secondary wavelet which travel with velocity of light (c).

Let t=> Time taken by the wavelets to reach from B to A’ and from A to B’.

                A’B’=> Reflected plane wave front.

                ∴ BA’ = ct and AB’ = ct

                ∴ BA’ = AB’-----------(1)

In ∆ ABA’ :

In ∆ AB’A’ :

Putting the value of BA’ and AB’ in equation (1), we get

                AA’ sin i = AA’ sin r

                ⟹ sin i = sin r

                ⟹ i = r

1. i.e. angel of incidence = angle of reflection
2. Further the incident waves, reflected waves and the normal all lie in the same plane (plane of paper).

Laws of refraction (On the basis of Huygen’s principle)

Let AB=> Plane wave front incident on surface XY separating the two media (air and glass).

Let µ=> Refractive index of glass w.r.t. air.

c=> Velocity of light in air.

𝜗=> Velocity of light in glass.

Let t=> Time taken by the secondary wavelets reach from B to A’ and A to B’.

∴ BA’ = ct and AB’ = 𝜗t

In ∆ BAA’:

In ∆ BAA’: 

Putting the value of BA’ and AB’ in equation (1) , we get

   <=  Snell’s haw of refraction.

1. i.e. ratio of sine of angle of incidence to the sine of angle of refraction is constant(µ) for two media in contact.
2. Further, the incident ray , refracted ray and the normal all lie in the same plane (plane of paper).