A physics class is challenged to determine the focal length of an unknown thin concave lens without using any converging lenses. The students are allowed a meterstick, an illuminated object of adjustable distance, and their own eyesight. They devise a procedure in which the object is moved to several positions along a ruler while the students record the apparent position of the virtual image by direct sighting.
Answer the following to design and evaluate their experimental method.
(1) Outline a step-by-step experimental procedure that would allow the students to obtain numerical values for both the object distance so and the (virtual) image distance si for multiple trials without using a screen.
(2) Derive an algebraic expression that the students can plot as a straight line whose slope or intercept yields the focal length of the lens. Clearly indicate which quantities are placed on each axis.
(3) Identify two significant sources of experimental uncertainty specific to this procedure and propose a method to minimize each one.
(4) Explain how the students could use their plotted data to evaluate whether the thin-lens approximation is valid for their lens over the range of distances tested.