Arrive at Snell's law of refraction, using Huygen's principle for refraction of a plane wave.

Explanation

AB=plane wave front
A.A=direction of propagation of wave front
PP.=surface of separation of medium 1 and 2
`v_1,v_2` = speeds of light in medium 1 and 2 respectively.
i=angle of incidence
r=angle of refraction
`tau`=time taken by the wave front to travel a distance BC
To determine the shape of the refracted wavefront a sphere of radius ,`v_2 tau` is drawn and CE = tangent plane if the refracted wave front.
Consider triangles ABC and AEC sin i = `(BC)/(AC)=(v_1tau)/(AC) , sin r = (AE)/(AC)=(v_2tau)/(AC)`
`(sin i)/(sinr)=(v_1tau)/(v_2tau)=v_1/v_2` ...(1)
If c=speed of light in vacuum then, `n_1=c/v_1, n_2=c/n_2`
`therefore` Equation (1) `rArr (sin i)/(sin r) =c/n_1 xx n_2/c =n_2/n_1`
`n_1 sin i = n_2 sin r` This is the required Snell.s law .