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Derive the laws of refraction from the concept (Huygen's principle) of the wavefront.
Solution

According to Huygen's principle of wavefront is as follow.
Let PP' represent the surface separating medium-$1$ and medium-$2$, as shown in figure.
And $v_{1}$ and $v_{2}$ represent the speed of light in medium-$1$ and medium-$2$ respectively and $v_{2}$
And a plane wavefront $\mathrm{AB}$ propagating in the direction $\mathrm{AA}^{\prime}$ incident on the interface of two medium at an angle $i$.
Let $\tau$ be the time taken by the wavefront to travel the distance $\mathrm{BC}$.
$\therefore \mathrm{BC}=v_{1} \tau$
In order to determine the shape of the refracted wavefront, draw a sphere of radius $v_{2} \tau$ from the point $A$ in the second medium (the speed of the wave in the second medium is $v_{2}$ and the distance covered in time $\tau$ is $v_{2} \tau$.)
Let $\mathrm{CE}$ represent a tangent plane drawn from the point $\mathrm{C}$ on the sphere. Then $\mathrm{AE}=v_{2} \tau$ and $\mathrm{CE}$ would represent the refracted wavefront.
According to Huygen's principle of wavefront is as follow.