An equiconvex glass lens $(a)$ has a focal length $f$ and power $P$. It is cut into two symmetrical halves $(b)$ by a plane containing the principal axis. The two pieces are recombined as shown in figure $(c)$. The power of the new combination is

An object is placed at a distance of $15\;cm$ from a convex lens of focal length $10\;cm$. On the other side of the lens,a convex mirror is placed such that the image formed by the combination coincides with the object itself. Find the focal length of the convex mirror if the distance between the lens and the mirror is $30\;cm$. (in $;cm$)

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

In the diagram given below,there are three lenses formed. Considering the negligible thickness of each of them as compared to $|R_1|$ and $|R_2|$,i.e.,the radii of curvature for the upper and lower surfaces of the glass lens,the power of the combination is:

$A$ point source of light is placed at $2f$ from a converging lens of focal length $f$. $A$ flat mirror is placed on the other side of the lens at a distance $d$ such that rays reflected from the mirror are parallel after passing through the lens again. If $f=30 \, cm$,then $d$ is equal to ............. $cm$.

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.