Problem 5.36

A source of light is located at a distance \(l=90 \mathrm{~cm}\) from a screen. A thin converging lens provides the sharp image of the source when placed between the source of light and the screen at two positions. Determine the focal length of the lens if (a) the distance between the two positions of the lens is \(\Delta l=\) \(=30 \mathrm{~cm}\) (b) the transverse dimensions of the image at one position of the lens are \(\eta=4.0\) greater than those at the other position.