$A$ point object is held above a thin equiconvex lens at its focus. The focal length is $0.1 \ m$ and the lens rests on a horizontal thin plane mirror. The final image will be formed at

An equiconvex lens of glass of focal length $0.1 \text{ m}$ is cut along a plane perpendicular to the principal axis into two equal parts. The ratio of the focal lengths of the new lenses formed is

$A$ concave mirror of focal length $f_1$ is placed at a distance of $d$ from a convex lens of focal length $f_2$. $A$ beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance $d$ must equal:

$A$ concave mirror of focal length $f_{1}$ is placed at a distance $d$ from a convex lens of focal length $f_{2}$. $A$ parallel beam of light coming from infinity parallel to the principal axis falls on the convex lens and then after refraction falls on the concave mirror. If the light is to retrace its path,the distance $d$ should be:

$A$ convex lens of focal length $30 \ cm$ is placed in contact with a concave mirror of focal length $20 \ cm$. What is the focal length of the system in $cm$?

$A$ point source is placed $20 \,cm$ to the left of a concave lens of focal length $10 \,cm$.
$(a)$ Where is the image formed?
$(b)$ Where to the right of the lens would you place a concave mirror of focal length $5 \,cm$,so that the final image is coincident with the source?
$(c)$ Where would the final image be formed,if the concave mirror is replaced by a plane mirror at the same position?