Question

A plane light wave propagating from a rarer into a denser medium, is incident at an angle i on the surface separating two media. Using Huygen’s principle, draw the refracted wave and hence verify Snell's law of refraction.

Answer 1

Here, v₁ and v₂ are speeds of light in medium 1 and 2 as shown BC = v₁t to get the shape of wave front draw an arc of radius v₂t form A towards medium 2.

If CE is tangent plane then AE = v₂t,

CE represents refracted wave front

In ΔABC, `sin i = (BC)/(AC) = (v_1t)/(AC)`

In ΔAEC, `sin r = (AE)/(AC) = (v_2t)/(AC)`

⇒ `(sin i)/(sin r) = v_1/v_2`   ...(i)

Also, `mu_1 = C/v_1; mu_2 = C/v_2`

⇒ `u_2/mu_1 = v_1/v_2`   ...(ii)

From (i) & (ii)

`(sin i)/(sin r) = mu_2/mu_1`

This is Snell''s law of refraction.