A lens is moved along the optical axis between a fixed object and a fixed image screen. Th...

A lens is moved along the optical axis between a fixed object and a fixed image screen. 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 = (L2 − D2)/4L. This is Bessel’s method for finding the focal length of a lens.

Figure 1