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) Starting with the mathematical relation that links the object distance, image distance, and focal length for a thin lens, derive an expression for the focal length f in terms of the fixed lamp-to-screen separation L and the measured separation d between the two lens positions.
(b) Use your derived expression to calculate the numerical value of the focal length for this lens. Include the correct units and algebraic sign.
(c) Discuss whether the lens is converging or diverging and explain how your calculation supports this conclusion.
(d) Identify one experimental factor that could introduce systematic error into this determination of f and describe how the error would affect the calculated focal length.
(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.