In the figure shown a concave mirror of focal length 50 cm is made to move downward with constant velocity of 4 m/sec. The level of water having $μ = \frac{4}{3}$ in also falling downward at speed of 2 m/sec. Inside the water the fish is moving upward with speed of 6 m/sec and is lying along principal axis of concave mirror. Find out the speed of image of fish which is formed after reflection through concave mirror at the instant shown

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18 m/sec downward

none of these

54 m/sec downward

36 m/sec downward

answer is B.

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Detailed Solution

For any outside stationary observer (Paraxial rays approx) the fish will be appeared at 15 cm from
surface and moving with speed of 4 cm/sec in upward direction
Now, $use {\vec{v}}_{1 m} = - m^{2} V_{Om}$
where m $= \frac{- 50}{- 50 + 30} = \frac{5}{2}$
$\begin{array}{l} \Rightarrow v_{1} - (- 4) = - \frac{25}{4} [4 - (- 4)] \\ \Rightarrow v_{1} + 4 = - 50 \\ \Rightarrow v_{1} = - 54 m / \sec \\ (- ve sign showing downward direction) \end{array}$