Question

A ray of light is travelling from glass of refractive index \( \frac{3}{2} \) to water of refractive index \( \frac{4}{3} \). What is the minimum angle of incidence for which no light enters into the water?

• A. \( i_c = \sin^{-1}\left(\frac{9}{8}\right) \)
• B. \( i_c = \sin^{-1}\left(\frac{8}{9}\right) \)
• C. \( i_c = \sin^{-1}\left(\frac{2}{3}\right) \)
• D. \( i_c = \sin^{-1}\left(\frac{1}{2}\right) \)

Hint:

Total internal reflection occurs only when light travels from denser to rarer medium.

Answer 1

The Correct Option is B

Step 1: Identify condition.
No light enters second medium \( \Rightarrow \) total internal reflection.

Step 2: Use critical angle formula.
\[ \sin i_c = \frac{n_2}{n_1} \]

Step 3: Identify refractive indices.
\[ n_1 = \frac{3}{2}, \quad n_2 = \frac{4}{3} \]

Step 4: Substitute values.
\[ \sin i_c = \frac{\frac{4}{3}}{\frac{3}{2}} \]

Step 5: Simplify expression.
\[ \sin i_c = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \]

Step 6: Write critical angle.
\[ i_c = \sin^{-1}\left(\frac{8}{9}\right) \]

Step 7: Final Answer.
\[ \boxed{\sin^{-1}\left(\frac{8}{9}\right)} \]