Question

A plane wavefront is travelling from air to glass, as shown in the diagram. The ratio of width of wavefront in air to that in glass, is

• A. $\frac{\sin i}{\sin r}$
• B. $\frac{\sin i}{\cos r}$
• C. $\frac{\cos i}{\sin r}$
• D. $\frac{\cos i}{\cos r}$

Answer 1

The correct option is D $\frac{\cos i}{\cos r}$


The ratio of width of wavefront in air to that in glass is equal to $\frac{AB}{A_1{B}_1}$

By the geometry of the figure,

In $\Delta AB{B}_1$
$\angle B{B}_{1}A=90-i$
and $\sin (90-i)=\frac{AB}{A{B}_1}$
$\therefore \cos i=\frac{AB}{A{B}_1}....\left(i\right)$

In $\Delta A{A}_1{B}_1$
$\angle A_{1}A{B}_1=90-r$
$\sin (90-r)=\frac{A_1{B}_1}{A{B}_1}$
$\therefore \cos r=\frac{A_1{B}_1}{A{B}_1}....\left(ii\right)$

From $\left(i\right)$ and $\left(ii\right)$, we can write,
$\frac{\cos i}{\cos r}=\frac{AB}{A_1{B}_1}$

Hence, $\left(D\right)$ is the correct answer.