$A$ 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:

$A$ plano-convex lens,when silvered at its plane surface,is equivalent to a concave mirror of focal length $28 \, cm$. When its curved surface is silvered and the plane surface is not silvered,it is equivalent to a concave mirror of focal length $10 \, cm$. Find the refractive index of the material of the lens.

An object is placed in front of a thin convex lens of focal length $30\, cm$ and a plane mirror is placed $15\, cm$ behind the lens. If the final image of the object coincides with the object,the distance of the object from the lens is.....$cm$.

$A$ point object is placed at a distance of $20 \ cm$ from a thin plano-convex lens of focal length $15 \ cm$. If the plane surface is silvered,then the image formed is:

$A$ thin plano-convex lens acts like a concave mirror of focal length $0.2 \ m$ when silvered from its plane surface. The refractive index of the material of the lens is $1.5$. The radius of curvature of the convex surface of the lens will be.......$m$.

$A$ 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 $m$)