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

The Correct Option is A

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: \(\sqrt{2} : 1\).