CUET · PHYSICS · PYQ PAPER 2023

A ray of light strikes a glass plate at an angle of \(60^{\circ}\). If the reflected and refracted rays are perpendicular to each other then the refractive index of glass is

A 1.53
B 1.732
C 1.42
D 1.32

Verified Solution

Answer & Solution

Correct Answer

(B) 1.732

Step-by-step Solution

Detailed explanation

\(\mu = \tan(i_p)\) \(\mu = \tan(60^{\circ})\) \(\mu = 1.732\)

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.

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Match List-I with List-II

List-I (Conditions)	List-II (Type of matrix)
(A) Square matrix \(A\)	(I) \(A=\left[a_{i j}\right]_{m \times m}\), where \(\left\{\begin{array}{ll}a_{i j}=0 & , i \neq j \\ a_{i j}=k & , i=j\end{array}\right.\) where \(k \neq 0\) is constant
(B) Scalar Matrix \(A\)	(II) \(A=\left[a_{i j}\right]_{m \times m}\)
(C) Diagonal matrix \(A\)	(III) \(A=\left[a_{i j}\right]_{m \times m}\), where \(\left\{\begin{array}{ll}a_{i j}=0 & , i \neq j \\ a_{i j}=1 & , i=j\end{array}\right.\)
(D) Identity matrix \(A\)	(IV) \(A=\left[a_{i j}\right]_{m \times m}\), where \(a_{i j}=0, i \neq j\)

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