Explain the refraction of a plane wave from a denser to a rarer medium using Huygens' principle.

(N/A) Consider a plane wavefront $AB$ incident at an angle $i$ on the interface separating two media. Let $v_{1}$ and $v_{2}$ be the speeds of light in the first (denser) and second (rarer) media,respectively,such that $v_{2} > v_{1}$.
According to Huygens' principle,each point on the wavefront $AB$ acts as a source of secondary wavelets. In time $\tau$,the point $B$ travels to $C$ with speed $v_{1}$,covering a distance $BC = v_{1}\tau$. Simultaneously,the secondary wavelets starting from $A$ travel a distance $AE = v_{2}\tau$ in the second medium.
Drawing a tangent from $C$ to the spherical wavelet of radius $v_{2}\tau$ centered at $A$,we get the refracted wavefront $CE$. From the geometry of the triangles $\triangle ABC$ and $\triangle AEC$:
$\sin i = \frac{BC}{AC} = \frac{v_{1}\tau}{AC}$
$\sin r = \frac{AE}{AC} = \frac{v_{2}\tau}{AC}$
Dividing the two equations:
$\frac{\sin i}{\sin r} = \frac{v_{1}}{v_{2}}$
Since $v_{2} > v_{1}$,it follows that $\sin r > \sin i$,which implies $r > i$. Thus,the refracted ray bends away from the normal when moving from a denser to a rarer medium. This is illustrated in the provided figure.