CUET · PHYSICS · PYQ PAPER 2023

One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).
What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?

A \(\sin ^{-1}\left(\frac{1}{4}\right)\)
B \(\sin ^{-1}\left(\frac{1}{2}\right)\)
C \(\sin ^{-1}\left(\frac{3}{4}\right)\)
D \(\sin ^{-1}\left(\frac{2}{3}\right)\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(\sin ^{-1}\left(\frac{3}{4}\right)\)

Step-by-step Solution

Detailed explanation

\(\sin \theta_c = \frac{n_L}{n_p} = \frac{3\sqrt{2}/4}{1.5} = \frac{3\sqrt{2}/4}{3/2} = \frac{\sqrt{2}}{2}\) \(\theta_c = 45^{\circ}\) \(r_2 = \theta_c = 45^{\circ}\) \(A = r_1 + r_2 \implies 75^{\circ} = r_1 + 45^{\circ} \implies r_1 = 30^{\circ}\)…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List-I with List-II

List -I Physical Quantity	List II Dimensional Formula
(A) Capacitance	(I) \( [M L^3 T^{-3} A^{-1}] \)
(B) Electric Flux	(II) \( [M L^2 T^{-3} A^{-1}] \)
(C) Potential	(III) \( [L^{-2} A T] \)
(D) Polarisation	(IV) \( [M^{-1} L^{-2} T^4 A^2] \)

Choose the correct answer from the options given below:

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One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?

Step-by-step Solution

One face of a prism of refractive index 1.5 and angle \(75^{\circ}\) is covered with a liquid of refractive index \(\frac{3 \sqrt{2}}{4}\).
What should be the angle of incidence of light on the clear face of prism for which light is just totally reflected at the liquid covered face?