JEE Advanced · Physics · 24. Ray Optics

A wide slab consisting of two media of refractive indices $n_{1}$ and $n_{2}$ is placed in air as shown in the figure. A ray of light is incident from medium $n_{1}$ to $n_{2}$ at an angle $θ$ , where $\sin θ$ is slightly larger than $\frac{1}{n_{1}}$ . Take refractive index of air as $1$ . Which of the following statement(s) is (are) correct?

A The light ray enters air if $n_{2} = n_{1}$ .
B The light ray is finally reflected back into the medium of refractive index $n_{1}$ if $n_{2} < n_{1}$ .
C The light ray is finally reflected back into the medium of refractive index $n_{1}$ if $n_{2} > n_{1}$ .
D The light ray is reflected back into the medium of refractive index $n_{1}$ if $n_{2} = 1$ .

Verified Solution

Answer & Solution

Correct Answer

(B) The light ray is finally reflected back into the medium of refractive index $n_{1}$ if $n_{2} < n_{1}$ .

Step-by-step Solution

Detailed explanation

Option A: If

(n_{1} = n_{2})

n_{1} \sin θ = n_{2} \sin θ_{1} . . . (1)

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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Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.

Column I	Column II
(A)The number of permutations containing the word ENDEA, is	(p) $5 !$
(B) The number of permutations in which the letter E occurs in the first and the last positions, is	(q) $2 \times 5!$
(C) The number of permutations in which none of the letters D, L, N occurs in the last five positions, is	(r) $7 \times 5!$
(D) The number of permutations in which the letters A, E, O occur only in odd positions, is	(s) $21 \times 5!$

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