Question

Critical angle of incidence for a pair of optical media is $45^\circ$.
The refractive indices of the first and second media are in the ratio:

• A. $\sqrt{2} : 1$
• B. $1 : 2$
• C. $1 : \sqrt{2}$
• D. $2 : 1$

Answer 1

Answer: (A)

$\sqrt{2} : 1$

Answer 2

The critical angle is given by:

$\sin C = \frac{n_2}{n_1}.$

At $C = 45^\circ$:

$\sin 45^\circ = \frac{1}{\sqrt{2}} = \frac{n_2}{n_1}.$

Thus:

$\frac{n_1}{n_2} = \sqrt{2} : 1.$

Final Answer: $\sqrt{2} : 1$.