Question

In the figure shown a concave mirror of focal length $50cm$ is made to move downward with constant velocity of $4mse{c}^{-1}$ . The level of water having $\mu =\frac{4}{3}$ in also falling downward at speed of $2mse{c}^{-1}$ . Inside the water the fish is moving upward with speed of $6mse{c}^{-1}$ 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. $36mse{c}^{-1}$ downward.
• B. $54mse{c}^{-1}$ downward.
• C. $18mse{c}^{-1}$ 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 $4cmse{c}^{-1}$ in upward direction
Now, use ${\overrightarrow{v}}_{Im}=-m^2{v}_{OM}$
where $m=\frac{-50}{-50+30}=\frac{5}{2}$
$\Rightarrow v_I-\left(-4\right)=-\frac{25}{4}\left[4-\left(-4\right)\right]$
$\Rightarrow v_I+4=-50$
$\Rightarrow v_I=-54mse{c}^{-1}$
(- $ve$ sign showing downward direction)