Question

A glass prism ABC (refractive index 1.5), immersed in water (refractive index \( \frac{4}{3} \)). A ray of light is incident normally on face AB. If it is totally reflected at face AC, then

• A. 40%
• B. 50%
• C. 65.6%
• D. 34.4%

Hint:

For total internal reflection to occur, the angle of incidence must be greater than the critical angle, which depends on the refractive indices of the two media.

Answer 1

The Correct Option is A

For total internal reflection to occur at face AC, the angle of incidence at face AC must be greater than the critical angle \( \theta_c \).
The critical angle is given by: \[ \sin \theta_c = \frac{n_{\text{water}}}{n_{\text{glass}}} \] where \( n_{\text{water}} = \frac{4}{3} \) and \( n_{\text{glass}} = 1.5 \). Substituting the values: \[ \sin \theta_c = \frac{\frac{4}{3}}{1.5} = \frac{4}{4.5} = 0.8889 \] Thus, \[ \theta_c = \sin^{-1}(0.8889) \approx 62^\circ \] Now, for the light incident normally on face AB, it will refract inside the prism.
The angle of incidence at face AC will depend on the refractive index and geometry of the prism.
The light will experience total internal reflection if the angle at face AC is greater than \( \theta_c \).
The fraction of light that is reflected depends on the refractive indices and the angle of incidence.
Based on these parameters, the correct fraction of light that gets totally reflected at face AC is approximately 40%.
Thus, the correct answer is (a).