A ball is dropped from a height of $20 \mathrm{~m}$ above the surface of water in a lake. The refractive…
A ball is dropped from a height of $20 \mathrm{~m}$ above the surface of water in a lake. The refractive index of water is $\frac{4}{3}$. A fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is $12.8 \mathrm{~m}$ above the water surface, the fish sees the speed of ball as
$9 \mathrm{~ms}^{-1}$
$12 \mathrm{~ms}^{-1}$
$16 \mathrm{~ms}^{-1}$
$21.33 \mathrm{~ms}^{-1}$
Solution
$v=\sqrt{2 g h}=\sqrt{2 \times 10 \times 7}=12 \mathrm{~ms}^{-1}$
In this case when eye is inside water, $x_{\text {app. }}=\mu x \Rightarrow \frac{d x_{\text {app. }}}{d t}=\mu \cdot \frac{d x}{d t}$ or $\quad v_{\text {app. }}=\mu v=\frac{4}{3} \times 12=16 \mathrm{~ms}^{-1}$
