Correct Option: Assertion (A) is true, but Reason (R) is false.

Step 1 (Governing Laws & Given Data): [0.5 Mark]

• For a prism with angle $A$, if a ray is incident normally on the first face, the angle of incidence at the second face is $r_2 = A$.
• The condition for the emergent ray to graze the surface is that the angle of incidence at the second face must equal the critical angle: $r_2 = C$.
• The critical angle $C$ is defined by the relation: $\sin C = \frac{1}{\mu}$.

Step 2 (Step-by-Step Mathematical Working): [0.25 Mark]

• Given: Ray is incident normally, so $i_1 = 0 \implies r_1 = 0$.
• From the prism relation $r_1 + r_2 = A$, we get $0 + r_2 = A \implies r_2 = A$.
• For grazing emergence, the angle of refraction at the second face is $e = 90^\circ$. By Snell's Law at the second interface: $$\mu \sin(r_2) = 1 \cdot \sin(90^\circ)$$ $$\sin(r_2) = \frac{1}{\mu}$$
• Since $\sin C = \frac{1}{\mu}$, it follows that $r_2 = C$. Substituting $r_2 = A$, we get $A = C$. Thus, Assertion (A) is True.
• Reason (R) states that the refractive index $\mu$ depends on the angle of the prism $A$. This is False; $\mu$ is a material property (dependent on the material of the prism and wavelength of light), whereas $A$ is a geometric parameter.

Step 3 (Final Concluded Answer): [0.25 Mark]

Since the Assertion is a correct derivation based on the geometry of the prism and the definition of critical angle, and the Reason provides a scientifically incorrect statement regarding the nature of refractive index, the correct choice is: Assertion (A) is true, but Reason (R) is false.

💡 EL10 Concept Insight: Think of the prism angle as the "gatekeeper" for the light; if the gate is tilted exactly at the critical angle, the light gets stuck sliding along the edge instead of escaping. However, the material's refractive index is like its "personality"—it stays the same regardless of how you cut or tilt the prism shape.