JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Geometrical Optics

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An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12 cm. when viewed from the opposite side, the apparent distance of the bubble is observed as 4 cm. If the side of the ice cube is 24 cm, the refractive index of the ice cube is

(A) $\frac{4}{3}$
(B) $\frac{3}{2}$ ✓ Correct
(C) $\frac{2}{3}$
(D) $\frac{6}{5}$

Answer: (B)

Solution

Using the relation for apparent depth:

d_{apparent} = \frac{d _{actual}}{μ}

. From one side:

12 = \frac{x}{μ}

, where

x

is the actual distance of the bubble from that side. From the opposite side:

4 = \frac{24 - x}{μ}

. From the first equation:

x = 12 μ

. Substituting into the second:

4 = \frac{24 - 12 μ}{μ}

, which gives

4 μ = 24 - 12 μ

, so

16 μ = 24

, yielding

μ = 1.5 = \frac{3}{2}

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Single correct option

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JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Geometrical Optics

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