The refractive indices of glass and water are \( 3/2 \) and \( 4/3 \), respectively. If light passes from glass to water, the critical angle is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sin^{-1}\left(\displaystyle\frac{8}{9}\right) \)
Light going from a denser medium (glass) to a rarer one (water) undergoes total internal reflection beyond the critical angle \( C \), at which the refracted ray grazes the surface, so the angle of refraction is \( 90^\circ \). Snell's law gives
\( \displaystyle n_{\mathrm{g}}\sin C = n_{\mathrm{w}}\sin 90^\circ \;\Rightarrow\; \sin C = \frac{n_{\mathrm{w}}}{n_{\mathrm{g}}} \)
\( \displaystyle \sin C = \frac{4/3}{3/2} = \frac{4}{3} \times \frac{2}{3} = \frac{8}{9} \)
\( \displaystyle C = \sin^{-1}\left(\frac{8}{9}\right) \)
Shortcut: The sine of an angle cannot exceed 1, so \( 10/9 \) and \( 9/8 \) are impossible and Options (3) and (4) can be rejected at once.