Question

A paperweight in the form of a hemisphere of radius $3.0cm$ is used to hold down a printed page. An observer looks at the page vertically through the paperweight. At what height above the page will the printed letters near the centre appear to the observer?

Answer 1

Given that

Radius of paper weight $\left(R\right)=3cm$

Refractive index of paper weight $\left({\mu }_2\right)=\frac{3}{2}$

Refractive index of air $\left({\mu }_1\right)=1$

In the first case refraction is at $A$

$\Rightarrow u=0,R=\infty$

We know that

$\Rightarrow \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{\frac{3}{2}}{v}-\frac{1}{0}=\frac{{\mu }_2-{\mu }_1}{\infty }$

$\Rightarrow v=0$

In the second case refraction is at $B$

$\Rightarrow u=-3cm,R=-3cm$

We know that

$\Rightarrow \frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\Rightarrow \frac{1}{v}-\frac{3}{2\times (-3)}=\frac{1-\frac{3}{2}}{-3}$

$\Rightarrow \frac{1}{v}+\frac{3}{6}=\frac{1}{6}$

$\Rightarrow \frac{1}{v}=\frac{-1}{3}$

$\Rightarrow =-3cm$

Hence there is no shift in final image