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 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.)

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