How is a wavefront defined? Using Huygen's construction , draw a figure showing the propagation of a plane wave refracting at a plane surface separating two media. Hence verify Snell's law of refraction.

Explanation

Wavefront : The continuous locus of all the particles of a medium, which are vibrating in the same phse is called a wavefront.
(ii) Snell's law of refraction : Let `PP'` represent the surface separating medium `1` and medium `2` as shown in fig.

Let `v_(1)` and `v_(2)` represents the speed of light in medium `1` and medium `2` respectively. We assume a plane wavefront `AB` propagating in the direction `A'A` incident on the interface at an angle `i.` Let `t` be the time taken by the wavefront to travel the distance `BC`.
`therefore BC=v_(1)t ["distance=speed"xx"time"],AE=v_(2)t`
`therefore CE` would represent the refracted wavefront.
In `Delta ABC` and `Delta AEC,` we have
`sini =(BC)/(AC)=(v_(1)t)/(AC)`
and `sinr=(AE)/(AC)=(v_(2)t)/(AC)`
where `i` and `r` the angles of incident and refraction respectively.
`therefore(sini)/(sinr)=(u_(1))/(AC).(AC)/(u_(2)t)`
`(sini)/(sinr)=(u_(1))/(u_(2))`
If `C` represents the speed of ligth in vacuum, then
`n_(1)=(C)/(u_(1)) and n_(2)=(C)/(u_(2)) rArr 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`.
`therefore (sini)/(sinr)=(C//n_(1))/(C//n_(2))rArr(sini)/(sinr)=(n_(2))/(n_(1))`
`rArrn_(1)sini=n_(2)sinr`
This is the Snell's law of refraction