Optics 2 Question 6
6. A ball is dropped from a height of $20 m$ 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 $12.8 m$ above the water surface, the fish sees the speed of ball as
(2009)
(a) $9 ms^{-1}$
(b) $12 ms^{-1}$
(c) $16 ms^{-1}$
(d) $21.33 ms^{-1}$
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Answer:
Correct Answer: 6. (c)
Solution:
- $v=\sqrt{2 g h}=\sqrt{2 \times 10 \times 7}=12 ms^{-1}$
In this case when eye is inside water,
$$ x _{\text {app. }}=\mu x $$
$$ \begin{aligned} \therefore & & \frac{d x _{\text {app. }}}{d t} & =\mu \cdot \frac{d x}{d t} \\ \text { or } & & v _{\text {app. }} & =\mu v=\frac{4}{3} \times 12=16 ms^{-1} \end{aligned} $$
