Question

A ball is dropped from a height of $20m$ above the surface of the water in a lake. The refractive index of water is $\frac{4}{3}$ . A fish inside the lake, in the line of fall of ball is looking at the ball. At an instant, when the ball is $12.8m$ above the water surface, the fish sees speed of ball as

• A. $9{\text{ m s }}^{-1}$
• B. $12{\text{ m s }}^{-1}$
• C. $16{\text{ m s }}^{-1}$
• D. $21.33{\text{ m s }}^{-1}$

Answer 1

Answer: (C)

$\upsilon =\sqrt{2\text{gh}}=\sqrt{2\times 10\times 7}$
$=12{\text{ms}}^{-1}$
In this case when eye is inside water,

$x_{\text{app.}}=\mu x$
$\therefore \frac{\text{d}{x}_{\text{app.}}}{\text{dt}}=\mu \cdot \frac{\text{d}x}{\text{dt}}$
or, ${\upsilon }_{\text{app.}}\mu \upsilon =\frac{4}{3}\times 12=16{\text{ m s }}^{-1}$