Question
Consider three media $P,Q$ and $R$ with refractive indices $1,1.25$, and 1.5 respectively. The medium $Q$ having a thickness of 5 cm is placed between extended media $P$ and $R$ as shown in the figure. An object $O$ is placed at the centre of medium $Q$. If viewed from medium $P$ near the normal direction, the apparent depth of $O$ is $h_{1}$. For similar observation from medium $R$, the apparent depth is $h_{2}$. The value of $\left| h_{1} - h_{2} \right|$, in cm, is:
Options
Solution
Sol. [Key Concept: Refraction through media and critical angle]
(i) When object $O$ is viewed from medium $P$,
Apparent depth $h_{1} = \frac{h_{\text{real}\text{~}}}{\mu} = \frac{2.5}{1.25} = 2\text{ }cm$
(ii) When object $O$ is viewed from medium $R$, Apparent depth $h_{2} = \ _{Q}\mu_{R} \times 2.5$
$$\begin{matrix} & \ = 2.5 \times \frac{1.5}{1.25} = 3\text{ }cm \\ & \ \therefore\left| h_{1} - h_{2} \right| = 1\text{ }cm \end{matrix}$$
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