Question

The refractive index of glass is \( \frac{3}{2} \) and that of water is \( \frac{4}{3} \). The critical angle for a ray of light going from glass to water is

• A. \( \sin^{-1}\!\left(\frac{4}{7}\right) \)
• B. \( \sin^{-1}\!\left(\frac{5}{8}\right) \)
• C. \( \sin^{-1}\!\left(\frac{2}{3}\right) \)
• D. \( \sin^{-1}\!\left(\frac{8}{9}\right) \)

Hint:

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

Answer 1

The Correct Option is D

Step 1: Write the condition for critical angle.
For light going from a denser medium to a rarer medium, \[ \sin C = \frac{\mu_{\text{rarer}}}{\mu_{\text{denser}}} \]

Step 2: Substitute the given refractive indices.
Here, glass is denser and water is rarer: \[ \mu_g = \frac{3}{2}, \quad \mu_w = \frac{4}{3} \] \[ \sin C = \frac{\mu_w}{\mu_g} = \frac{\tfrac{4}{3}}{\tfrac{3}{2}} = \frac{4}{3}\times\frac{2}{3} = \frac{8}{9} \]

Step 3: Write the critical angle.
\[ C = \sin^{-1}\!\left(\frac{8}{9}\right) \]