Question

A rectangular slab of refractive index $\mu$ is placed over another slab of refractive index 3, both slabs being identical in dimensions. If a coin is placed below the lower slab, for what value of $\mu$ will the coin appear to be placed at the interface between the slabs when viewed from the top

• A. 1.8
• B. 2
• C. 1.5
• D. 2.5

Answer 1

Answer: (C)

. 1.5.

Let the dimension of the slabs be x.
The refractive index of a medium is also given by $=\frac{\text{Real depth}}{\text{Apparent depth}}$.
Apparent depth of coin as seen from top =$\frac{x}{{\mu }_1}+\frac{x}{{\mu }_2}=x$
$\Rightarrow \frac{1}{{\mu }_1}+\frac{1}{{\mu }_2}=1\Rightarrow \frac{1}{3}+\frac{1}{\mu }=1\Rightarrow \mu =1.5$.