## An object of height h approaches a concave mirror of focal length f along its axis…

An object of height h approaches a concave mirror of focal

length f along its axis with constant speed v, from an initial

distance s_{0} >> 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 s_{0}, v and t. The

result is fairly simple looking and should ‘blow up’ when s = f as

expected.)