A bird flying above a pond starts moving vertically down towards the water below at a speed of v m/s. Find its apparent velocity as viewed by a fish located at a depth of d m below the surface of water.

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Solution

we know equation of apperent height,
d/D = n(medium containing observer) / n(medium containing object)
(d - apparent height, D real height)
n(medium containing observer (here fish)) = μ
n(medium containing object (here bird)) = 1 (air is 1)
d/D = μ
d = μD
d/t = μD/t (divided both side with time ,t)
v' = μv (since distance/time is velocity)
(v' - apparent velocity, v = real velocity)
So answer is v' = μv
(Read twice if you can't understand)

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