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 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.....$cm$.

If a lens is cut into two pieces perpendicular to the principal axis and only one part is used,the intensity of the image

$A$ 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 $f = \dots \, cm$.

The figure shows an equiconvex lens of focal length $f$. If the lens is cut along $AB$,the focal length of each half will be

The radius of the curved surface of a plano-convex lens is $20 \, cm$ and the refractive index of the lens material is $1.5$. Calculate the equivalent focal length of the lens if the curved surface is silvered.