A vessel of depth ' d ' is half filled with oil of refractive index n₁ and the other half is filled with water of refractive index n₂. The apparent depth of this vessel when viewed from above will be- (a) (2d(n₁+n₂))/(n₁ n₂) (b) (d(n₁+n₂))/(2n₁ n₂) (c) (d n₁ n₂)/(2(n₁+n₂)) (d) (d n₁ n₂)/((n₁+n₂))

Answer: (b). Each layer has thickness d/2; apparent depth D = (d/2)/(n₁) + (d/2)/(n₂). D = d/2·(n₁ + n₂)/(n₁ n₂) = (d(n₁ + n₂))/(2n₁ n₂). So the answer is (b).

A vessel of depth ' d ' is half filled with oil of refractive index… | JEE Main 2023 (13 Apr, Shift 1)

Q37JEE Main 2023 · 13 APR · SHIFT 1Medium

Refraction, Glass Slab & Apparent Depth

A vessel of depth ' $d$ ' is half filled with oil of refractive index $n_1$ and the other half is filled with water of refractive index $n_2$ . The apparent depth of this vessel when viewed from above will be-

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Answer: (b)

Each layer has thickness $\dfrac{d}{2}$ ; apparent depth $D = \dfrac{d/2}{n_1} + \dfrac{d/2}{n_2}$ .
$D = \dfrac{d}{2}\cdot\dfrac{n_1 + n_2}{n_1 n_2} = \dfrac{d(n_1 + n_2)}{2n_1 n_2}$ .
So the answer is (b).

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Refraction, Glass Slab & Apparent Depth question from JEE Main 2023 (13 Apr, Shift 1)

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