MHTCET 17 Apr 2026 Shift 2 Paper

Concept:When the emergent ray just grazes the adjacent face, the angle of emergence is $90^\circ$, so the refracted ray inside the prism strikes the second face at the critical angle.Explanation:For an equilateral glass prism, the angle of prism is $A = 60^\circ$.The refractive index of glass is $\mu = \sqrt{2}$.Since the emergent ray just grazes the adjacent face, we have $e = 90^\circ$.Applying Snell's law at the second face of the prism:$$\mu \sin r_2 = \sin 90^\circ$$$$\sqrt{2} \sin r_2 = 1$$$$\sin r_2 = \frac{1}{\sqrt{2}}$$Therefore, $r_2 = 45^\circ$.For a prism, the relation between the angles of refraction is $r_1 + r_2 = A$.$$r_1 + 45^\circ = 60^\circ$$$$r_1 = 15^\circ$$Now applying Snell's law at the first face:$$\sin i = \mu \sin r_1$$$$\sin i = \sqrt{2} \sin 15^\circ$$$$i = \sin^{-1}\left(\sqrt{2} \sin 15^\circ\right)$$Answer:The angle of incidence is $i = \sin^{-1}\left(\sqrt{2} \sin 15^\circ\right)$, which corresponds to Option A.