Question

A narrow beam of light passing through the hemisphere of material with refractive index $n$, intersects at point $O$. Where does the beam converge (i.e. $y$ in $cm$ ) if the beam were to travel in the opposite direction as shown in figure $(b)$?
The value of $x$ is given to be $10cm$. Radius of the hemisphere is also $10cm$.

Answer 1

Answer: 5

$\frac{1}{v}-\frac{n}{\infty }=\frac{1-n}{-R}$
$10=v=\frac{R}{n-1}=\frac{10}{n-1}$
$\Rightarrow n=2$
$\frac{2}{v_1}-\frac{1}{\infty }=\frac{2-1}{10}$
$v_1=20cm$
$d_0=10cm$
$\frac{10}{2}=\frac{dI}{1}$
$\Rightarrow d_I=5cm$