Physics - Geometrical Optics Question with Solution | TestHub

Image formed by lens
$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$
$\Rightarrow \frac{1}{v}+\frac{1}{30}=\frac{1}{20}$
$\Rightarrow \frac{1}{v}=\frac{1}{20}-\frac{1}{30}$
$\Rightarrow v=60\mathrm{c}\mathrm{m}$
In the image remains at the same position even if the concave mirror is removed indicates that the image formed by lens is formed at the center of curvature of spherical mirror.
$\therefore$Radius of curvature of mirror$=80-60=20\mathrm{c}\mathrm{m}$
Focal length,$f=10\mathrm{c}\mathrm{m}$
For virtual image to be formed, object is to be kept between focus and pole. Hence, the maximum distance of object from spherical mirror for which virtual image is formed will be its focal length 10cm