Question

In the figure shown a concave mirror of focal length $50cm$ is made to move downward with constant velocity of $4msec^{- 1}$ . The level of water having $\mu =\frac{4}{3}$ in also falling downward at speed of $2msec^{- 1}$ . Inside the water the fish is moving upward with speed of $6msec^{- 1}$ 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

• A. $36msec^{- 1}$ downward.
• B. $54msec^{- 1}$ downward.
• C. $18msec^{- 1}$ downward.
• D. None of these.

Answer 1

Answer: (B)

For any outside stationary observer (Paraxial rays approx) the fish will be appeared at $15cm$ from surface and moving with speed of $4cmsec^{- 1}$ in upward direction
Now, use $\overset{ \rightarrow }{v}_{I m}=-m^{2}v_{O M}$
where $m=\frac{- 50}{- 50 + 30}=\frac{5}{2}$
$\Rightarrow v_{I}-\left(- 4\right)=-\frac{25}{4}\left[4 - \left(- 4\right)\right]$
$\Rightarrow v_{I}+4=-50$
$\Rightarrow v_{I}=-54msec^{- 1}$
(- $ve$ sign showing downward direction)