Question

An object of height h approaches a concave mirror of focal length f along its axis with constant speed v, from an initial distance s₀ >> R away. Determine the rate of change of the image height, dy'/dt, as a function of these variables and time. (Suggestion: differentiate the lens and magnification equations implicitly, and work with s, s′, f as long as possible to get dy′/dt in terms of h, s, s′, f and ds/dt first. Then eliminate s′ in favour of f and s, simplify and only at the end replace s and ds/dt in terms of s₀, v and t. The result is fairly simple looking and should ‘blow up’ when s = f as expected.)

Answer 1