$A$ 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 $cm$?

Given a thin convex lens (refractive index $\mu_2$),kept in a liquid (refractive index $\mu_1, \mu_1 < \mu_2$) having radii of curvature $|R_1|$ and $|R_2|$. Its second surface is silver-polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place?

$A$ thin equiconvex lens has a focal length of $10\; cm$ and a refractive index of $1.5$. One of its faces is now silvered,and for an object placed at a distance $u$ in front of the lens,the image coincides with the object. The value of $u$ is: (in $; cm$)

$A$ thin plano-convex lens made of glass of refractive index $1.5$ is immersed in a liquid of refractive index $1.2$. When the plane side of the lens is silver-coated for complete reflection,the lens immersed in the liquid behaves like a concave mirror of focal length $0.2 \ m$. The radius of curvature of the curved surface of the lens is: (in $m$)

The final image of the object forms on the object itself. If the focal length of the lens is $30 \ cm$,then the radius of curvature of the mirror is .... $cm$.

$A$ 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: