Question Analysis: A ray of light is incident normally on face AB of a prism ABC. We must determine the behavior of the ray at face AC.

Step 1 (Formula / Governing Law & Given Data): [1 Mark]

• Refractive index of the prism, $\mu = \sqrt{2}$.
• Refractive index of the surrounding medium (air), $\mu_a = 1$.
• The critical angle $i_c$ for the glass-air interface is given by the formula: $$\sin(i_c) = \frac{1}{\mu}$$

Step 2 (Step-by-Step Mathematical Working): [2 Marks]

• Since the ray is incident normally on face AB, it enters the prism undeviated.
• By geometry of the prism (assuming an isosceles right-angled prism where $\angle B = 90^\circ$, $\angle A = 45^\circ$, and $\angle C = 45^\circ$), the angle of incidence $i$ at face AC is equal to the angle of the prism, $i = 45^\circ$.
• Calculate the critical angle $i_c$: $$\sin(i_c) = \frac{1}{\sqrt{2}}$$ $$i_c = 45^\circ$$
• Compare the angle of incidence $i$ with the critical angle $i_c$: $$i = 45^\circ \text{ and } i_c = 45^\circ$$ Since $i = i_c$, the ray strikes the interface at the critical angle.

Step 3 (Final Concluded Answer): [1 Mark]

• When the angle of incidence equals the critical angle ($i = i_c$), the light ray is refracted at an angle of $90^\circ$ with the normal.
• Therefore, the ray will just graze along the face AC.
• Correct Option: (B)

💡 EL10 Concept Insight: Think of the critical angle as the "tipping point" for light; when light hits the glass surface at exactly this angle, it doesn't have enough energy to escape into the air, so it gets stuck sliding perfectly along the surface instead.