Question

A postage stamp placed under a glass, appears raised by $8mm.$ If refractive index of glass is $1.5$, calculate the actual thickness of the glass slab.

Answer 1

Step 1: Given data

1. A stamp appears raised by $8mm.$
2. The refractive index of glass is $1.5$.

Step 2: Calculate the actual thickness of the glass slab,

Let the real thickness of the glass slab be $xmm.$

Then, the apparent thickness will be $(x-8)mm.$

As we know,

$\mu =\frac{\text{Real depth}}{\text{Apparent depth}}$

On substituting the given values, we get

$$\begin{gathered} 1.5=\frac{x}{x-8} \\ 1.5x-12=x \\ 0.5x-12=0 \\ \begin{array}{r}\frac{0.5x}{0.5}=\frac{12}{0.5}\\ x=24mm\end{array} \end{gathered}$$

Hence, the actual thickness of the glass slab is $24mm.$