Question

The critical angle for glass-water interface (if \( \mu_g = \frac{3}{2}, \mu_w = \frac{4}{3} \)) is:

• A. \( \sin^{-1}\left(\frac{8}{9}\right) \)
• B. \( \sin^{-1}\left(\frac{9}{8}\right) \)
• C. \( \sin^{-1}\left(\frac{3}{2}\right) \)
• D. None of these

Hint:

Critical angle uses \(\frac{\text{rarer}}{\text{denser}}\) and must always be \(< 1\).

Answer 1

The Correct Option is A

Concept: \[ \sin C = \frac{\mu_{\text{rarer}}}{\mu_{\text{denser}}} \]
Step 1:
Glass is optically denser than water. \[ \sin C = \frac{\mu_w}{\mu_g} = \frac{4/3}{3/2} \]
Step 2: \[ \sin C = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \] \[ C = \sin^{-1}\!\left(\frac{8}{9}\right) \]