Question

A convex lens is placed between an object and a screen which are at a fixed distance apart for one position of the lens. The magnification of the image obtained on the screen is `m_(1)`. When the lens is moved by a distance d the magnification of the image obtained on the same screen `m_(2)`, Find the focal length of the lens.

Answer 1

If `D` is the distance between the object and the screen , d the separation of two position of lens throwing two images on the screen then
`m_(1) = ((D+d))/((D-d)) "and" m_(2) = ((D-d))/((D+d)) therefore m_(1) - m_(2) = (4Dd)/(D^(2) - d^(2))/(4D) = f "so" m_(1) - m_(2) = (d)/(f) implies f= (d)/(m_(1) -m_(2))`