Ray Optics

JEE Main level, single correct, medium

167 of 295

Question 167 of 295

An ice cube has a bubble inside. When viewed from one side the apparent distance of the bubble is 12cm12cm. When viewed from the opposite side, the apparent distance of the bubble is observed as 4cm4cm. If the side of the ice cube is 24cm24cm, the refractive index of the ice cube is

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Answer: (A) 32\dfrac{3}{2}

Let's assume that the original position of the bubble is xx from one side of the ice cube of side aa.
When the bubble is seen from one side, it can be written that
xμ=12...(1)\dfrac{x}{\mu }=12...\left(1\right)
For the view from the other side, it can be written that
a−xμ=4...(2)\dfrac{a-x}{\mu }=4...\left(2\right)
From equations (1) and (2), it is given that
24−12μ=4μ⇒μ=2416=1.5\begin{matrix}24-12\mu & = & 4\mu \\ & \Rightarrow & \mu =\dfrac{24}{16} \\ & = & 1.5\end{matrix}

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