Question

A curved thick glass surface is silvered at curved face and is not silvered on plane surface. Object is placed at $A$ as shown in the figure. Consider $P$ (pole of the silvered surface) as origin. If $x$ co-ordinate of final image is $(2 n)$. $cm$, then find $n$.

Answer 1

$u=-\left(4+\frac{4}{2}\right) \times 2=-12 \,cm $
$\frac{1}{v}+\frac{1}{-12}=\frac{1}{-8} $
$\Rightarrow v=-24 \,cm$
For final image (refraction through plane surface), we can write
$24=2\left(\frac{x}{1}+\frac{4}{2}\right)$
$ \Rightarrow 24=2 x+4 $
$x=10 \,cm$
so, distance from $P$ is $14\, cm$.