Question

Use Huygen's principle to show how a plane wavefront propogates from a denser to rarer medium. Hence verify Snell's law of refraction.

Answer 1

Consider the diagram given below of a plane wavefront propagating from a denser to rarer medium.


In $△ABC$,

$sini=\frac{BC}{AC}=\frac{v_{1}t}{AC}$

In $△CEA$,

$sinr=\frac{AE}{AC}=\frac{v_{2}t}{AC}$

$\therefore \frac{sini}{sinr}=\frac{BC}{AE}=\frac{v_{1}t}{v_{2}t}=\frac{v_1}{v_2}$

$\therefore {\mu }_1=\frac{c}{v_1}$

${\mu }_2=\frac{c}{v_2}$

$\therefore \frac{{\mu }_2}{{\mu }_1}=\frac{v_1}{v_2}$

$\therefore \frac{sini}{sinr}=\frac{{\mu }_2}{{\mu }_1}$

or ${\mu }_{2}sinr={\mu }_{1}sini$.

It is Snell's law.