Question

A point object $O$ is placed at a distance of $30cm$ from the pole of the convex mirror of focal length $20cm$ as shown in the figure. Find the final image distance

Answer 1

The ray coming from the object $O$ are incident of the convex mirrior. The image distance $v$ can be calculatedputting $u=-30cm$, $f=+20cm$ in
$\frac{1}{u}+\frac{1}{v}=\frac{1}{f}$
$\Rightarrow \frac{1}{-30}+\frac{1}{v}=\frac{1}{+20}$ $\Rightarrow \frac{1}{v}=\frac{1}{20}+\frac{1}{30}=+\frac{3+2}{60}=+\frac{1}{12}$
$\Rightarrow v=+12cm$
$\therefore$ The image $l$ is formed at a distance $u+v=30+12=42cm$ form $O$.
This image $l$ behaves as an object
$\Rightarrow$ This object $l$ after being refracted at surface $1$ forms an image $l$.
$\frac{Ol}{Ol}=\frac{1}{1.5}=\frac{2}{3}$ $\Rightarrow Ol=42\times \frac{2}{3}=28cm$.