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

Explanation

Let XY represent the surface separating the medium-I and medium-II.
Let `v_(1) and v_(2)` be the speed of light in medium-I and medium-II respectively.
Consider a plane wave front AB incident in medium-I at an angle i.
Let the secondary wavelet from B strike the surface XY at C in a time t, then `BC = v_(1) t` Secondary wavelet from A will travel a distance `v_(2) t` in medium-II in the same time t.
Therefore with A as centre and `v_(2) t` as radius draw an arc in the medium II. The tangent from C touches the are at D.
Let r be the angle of refraction.
`From triangle ^ "le" ABC, sin i = (BC)/ (AC) = (v_(1) t)/ (AC)`
`triangle ^ "le" ABC, sin r = (AD)/ (AC) = (v_(2) t)/ (AC)`
`(sin i)/ (sin r)= (v_(1) t)/ (AC) times (AC)/(v_(2) t) = (v_(1))/(v_(2))`
If c respresents the speed of light in vacuum then,
`n_(1) = (c)/(v_(1)) and n_(2) = (c)/(v_(2))`
`(n_(2))/(n_(1)) = (c)/(v_(2)) times (v_(1))/(c) = (v_(1))/(v_(2))`
`therefore (sin i)/(sin r) = (n_(2))/(n_(1))`
`n_(1) sin i = n_(2) sin r`
This is the Snell.s law of refraction