An equiconvex lens has power $P$. It is cut into two symmetrical halves by a plane containing the principal axis. The power of one part will be

Consider a concave mirror and a convex lens (refractive index $=1.5$) of focal length $10 \ cm$ each,separated by a distance of $50 \ cm$ in air (refractive index $=1$) as shown in the figure. An object is placed at a distance of $15 \ cm$ from the mirror. Its erect image formed by this combination has magnification $M_1$. When the setup is kept in a medium of refractive index $7/6$,the magnification becomes $M_2$. The magnitude $\left|\frac{M_2}{M_1}\right|$ is

$A$ glass slab of thickness $6 \, cm$ is silvered at one surface. An object is placed at a distance of $8 \, cm$ from the first surface. The image is formed at a distance of $12 \, cm$ behind the silvered surface. Find the refractive index of the glass.

An equiconvex lens of focal length $f$ is cut into four equal parts and two parts are placed as shown in the figure. The focal length of the system shown in the figure is:

An object is placed at a distance of $30\,cm$ from a convex lens of focal length $20\,cm$. At what distance (in $cm$) from the lens on the other side should a convex mirror of radius of curvature $10\,cm$ be placed so that the images formed by the lens and the mirror coincide?

$A$ biconvex lens of focal length $15 \,cm$ is in front of a plane mirror. The distance between the lens and the mirror is $10 \,cm$. $A$ small object is kept at a distance of $30 \,cm$ from the lens. The final image is