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 .

Question

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

TestHub · Accepted Answer

Let's assume that the original position of the bubble is $x$ from one side of the ice cube of side $a$ .

When the bubble is seen from one side, it can be written that

$\frac{x}{μ} = 12 . . . (1)$

For the view from the other side, it can be written that

$\frac{a - x}{μ} = 4 . . . (2)$

From equations (1) and (2), it is given that

$\begin{array}{rcl} 24 - 12 μ & = & 4 μ \\ \Rightarrow & μ = \frac{24}{16} \\ = & 1.5 \end{array}$

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