UPSC NDA I 2026 General Ability Paper

Concept:For a light ray to retrace its path after reflection from a mirror, it must strike the mirrored surface normally (perpendicularly).Explanation:1. Total Internal Reflection (TIR): The critical angle for the glass is $\theta_c = \sin^{-1}(1/\mu) = \sin^{-1}(1/1.5) \approx 41.8^\circ$. The light is incident at surface $AB$ from inside at an angle of incidence $i = \pi/3 = 60^\circ$. Since $i > \theta_c$, the ray undergoes total internal reflection.2. Angle with Surface $AB$: By the law of reflection, the angle of reflection is also $60^\circ$ with the normal. Thus, the reflected ray makes an angle of $90^\circ - 60^\circ = 30^\circ$ (or $\pi/6$) with the surface $AB$.3. Condition to Retrace Path: The ray travels towards the polished surface $BC$. To retrace its path, it must strike surface $BC$ at an angle of $90^\circ$ (normal incidence).4. Geometric Calculation: A right-angled triangle is formed by the incident ray, surface $AB$, and surface $BC$. The angles inside this triangle are the angle the ray makes with $AB$ ($30^\circ$), the angle at which it strikes $BC$ ($90^\circ$), and the angle $\theta$ between $AB$ and $BC$.Using the angle sum property of a triangle:$$30^\circ + 90^\circ + \theta = 180^\circ$$$$\theta = 60^\circ = \pi/3$$Answer:The correct angle $ABC$ ($\theta$) is $\pi/3$.