$2-27$ A lens is moved along the optical axis between a nxed

object and a fixed image sereen. The object and image

positions are separated by a distance $L$ that is more than

four times the focal length of the lens. Two positions of

the lens are found for which an image is in focus on the

screen, magnified in one case and reduced in the other. If

the two lens positions differ by distance $D,$ show that the

focal length of the lens is given by $f=\frac{L^2-D^2}{4}L.$

This is Bessel's method for finding the focal length of a

lens.