Question

A ray of light is incident normally on a prism ABC of refractive index \( \sqrt{2} \), as shown in the figure. After it strikes face AC, it will

• A. \( \) go straight und deviated
• B. \( \) just graze along the face AC
• C. \( \) refract and go out of the prism
• D. \( \) undergo total internal reflection

Hint:

For total internal reflection to occur, the angle of incidence inside the prism must be greater than the critical angle. In this case, the angle is \( 60^\circ \), which is greater than the critical angle of \( 45^\circ \), so total internal reflection occurs.

Answer 1

The Correct Option is D

Step 1: The ray of light is incident normally on the prism at point \( B \), which means that the angle of incidence \( i = 0^\circ \) on face \( AB \). Step 2: After striking face \( AC \), the angle of incidence \( \theta \) will be equal to the angle \( \angle ABC = 60^\circ \) because of the geometry of the prism. Step 3: The refractive index \( \mu = \sqrt{2} \), and for total internal reflection to occur, the angle of incidence at face \( AC \) must exceed the critical angle. The critical angle \( \theta_c \) is given by: \[ \sin \theta_c = \frac{1}{\mu} \] Substituting \( \mu = \sqrt{2} \): \[ \sin \theta_c = \frac{1}{\sqrt{2}} \Rightarrow \theta_c = \sin^{-1}\left( \frac{1}{\sqrt{2}} \right) = 45^\circ \] Step 4: Since the angle of incidence on face \( AC \) is \( 60^\circ \), which is greater than the critical angle \( 45^\circ \), the ray undergoes total internal reflection inside the prism. Conclusion: The correct answer is (D) undergo total internal reflection.