The radii of curvature of a double convex lens are $4 \ cm$ and $8 \ cm$. If the refractive index of the material of the lens is $1.5$,the focal length of the lens is nearly (in $cm$)

Write the lens formula for a thin lens.

When an object is at a distance $u_1$ and $u_2$ from a lens,a real image and a virtual image are formed,respectively,having the same magnification $m$. The focal length of the lens is:

$A$ screen is placed $100 \,cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \,cm$. The focal length of the lens is (in $\,cm$)

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

$A$ film projector magnifies a film onto a screen of area $100 \, cm^2$. If the linear magnification is $4$,what will be the area of the image on the screen in $cm^2$?