A physics laboratory uses the following procedure to measure the focal length of a thin lens. A bright lamp, the lens, and a movable screen are arranged along a straight optical rail. The lamp and screen are fixed 80.0 cm apart. By sliding the lens along the rail, students find two distinct positions, separated by 20.0 cm, at which a sharp image of the lamp appears on the screen.
(a) Derive an expression for f in terms of L and d.
(b) Calculate the focal length using L=80.0cm and d=20.0cm, including sign and units.
(c) State and justify whether the lens is converging or diverging.
(d) Identify a potential systematic error and describe its effect on the calculated focal length.