Question

A source of light is located at a distance l = 90 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 Δl = 30 cm; 

(b) the transverse dimensions of the image at one position of the lens are η = 4.0 greater than those at the other position.

Answer 1

The distance between the object and the image is l. Let x = distance between the object and the lens. Then, since the image is real, we have in our convention, u = -x, v = l - x

(a) If the distance between the two positions of the lens is Δl, then clearly

(b) The two roots are conjugate in the sense that if one gives the object distance the other gives the corresponding image distance (in both cases). Thus the magnifications are