Question

Light travels from an optically denser medium $A$ into the optically rarer medium $B$ with speeds $1.8\times10^8\,\text{m s^{-1}$ and $2.7\times10^8\,\text{m s}^{-1}$ respectively. The critical angle between them is ($\mu_1$ and $\mu_2$ are the refractive indices of media $A$ and $B$ respectively)}

• A. $\sin^{-1}\left(\dfrac{2}{3}\right)$
• B. $\sin^{-1}\left(\dfrac{3}{4}\right)$
• C. $\tan^{-1}\left(\dfrac{2}{3}\right)$
• D. $\tan^{-1}\left(\dfrac{3}{4}\right)$

Hint:

Critical angle depends only on the ratio of refractive indices of the two media.

Answer 1

The Correct Option is A

Step 1: Relation between refractive index and speed.
\[ \mu = \frac{c}{v} \]
Step 2: Calculating refractive indices.
\[ \mu_1 = \frac{c}{1.8\times10^8}, \quad \mu_2 = \frac{c}{2.7\times10^8} \]
Step 3: Formula for critical angle.
\[ \sin C = \frac{\mu_2}{\mu_1} = \frac{1.8}{2.7} = \frac{2}{3} \]
Step 4: Conclusion.
\[ C = \sin^{-1}\left(\frac{2}{3}\right) \]