$A$ plano-convex lens made of material of refractive index $\mu$ with radius of curvature $R$ is silvered on the curved side. How far away from the lens-mirror must you place a point object,so that the image coincides with the object?

$A$ planoconvex 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 $10 \ cm$. The refractive index of the material of the lens is:

The diagram shows a silvered equiconvex lens. An object of length $1\,cm$ is placed at a distance of $30\,cm$ in front of the lens. What will be the final image properties? The refractive index of the lens is $\mu$ and the refractive index of the medium in which the lens has been placed is $2\mu$. Both surfaces have a radius of curvature $R$.

$A$ prism having a refractive index $1.414$ and a refracting angle $30^{\circ}$ has one of its refracting surfaces silvered. $A$ beam of light incident on the other refracting surface will retrace its path if the angle of incidence is: (in $^{\circ}$)

$A$ convex lens of focal length $20 \, cm$ and a concave mirror of focal length $f$ are placed coaxially at a distance of $5 \, cm$ apart. $A$ parallel beam of light incident on the convex lens emerges from the system as a parallel beam. Then $f = \dots \, cm$.

$A$ 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 $m$)