Use Huygen's principle to show how a plane wavefront propagates from a denser to rarer medium. Hence verift snell's law of refreaction.

Explanation

Wavefront : The continuous locus of all the particles of a medium, which are vibrating in the same phase is called a wavefront.
(ii) Snell's law of refraction : Let PP' respresent the surface separating medium 1 and medium 2 as show in fig.
Let `v_(1) and v_(2)` represent the speed of light in medium. 1 and medium 2 respectively, we assume a pane wavefront AB propagating in the directionA , A incident on the interface at an angle i, Let t be the time taken by the wavefront to travel the distance BC.
BC= `v_(1)` t [ distance = speed` xx` time ]
In order to determine the shape of the refracted wavefront, we draw shphere of radius `v_(2)` t from the point C. then
` AE =v_(2)t`
CE would represent the refracted wavefront.
in ` triangleABC and triangleAEC` we have
` sin i = (BC)/(AC) = (v_(1)t)/(AC) and sin r= (AE)/(AC) = (v_(2)t)/(AC)`
where i and r are the angles of incident and refraction respectively .
` sin i/sin r = 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) Rightarrow v_(1) = C/n_(1) and v_(2) =C/n_(2)`
where `n_(1) and n_(2)` are the refractive indices of medium 1 and medium 2.
` sin i/sin r = (C//n_(1))/(C//n_(2)) Rightarrow sini/sinr = n_(2)/n_(1) Rightarrow n_(1) sin i =n_(2) sin r`.
This is the Snell's law of refraction.