Case: Read the passage and answer the question.
Total internal reflection is the reflection of light back into the denser medium at its interface with a rarer medium. For it to occur, light must travel from the denser medium towards the rarer medium, and the angle of incidence in the denser medium must be greater than the critical angle for the pair of media. The critical angle depends on the nature of the media and on the wavelength of light. It can be shown that \( \mu=1/\sin C \), where C is the critical angle.
The critical angle for a glass-air interface, where the refractive index of glass is \( \mu=3/2 \), is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( 42^\circ \) (approximately)
The passage gives the relation between the refractive index of the denser medium and the critical angle C for its interface with air. This relation is \( \mu=1/\sin C \). So \( \sin C \) is the reciprocal of the refractive index of glass.
\( \begin{aligned} \sin C &= \frac{1}{\mu} \\ &= \frac{1}{3/2} \\ &= \frac{2}{3} \\ &\approx 0.667 \end{aligned} \)
\( \begin{aligned} C &= \sin^{-1}(0.667) \\ &\approx 41.8^\circ \end{aligned} \)
Therefore, the critical angle for the glass-air interface is about \( 42^\circ \).