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Question

A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 43. 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

A
21.33 ms1
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B
16 ms1
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C
12 ms1
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D
9 ms1
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Solution

The correct option is B 16 ms1
Given that,
Refractive index of air, μ1=1
Refractive index of water, μ2=43
Height of drop of ball, H=20 m

When the ball is 12.8 m above the water surface, it has fallen through (h=2012.8=7.2 ms)

Thus, velocity at this instant is
v=2gh
v=2×10×7.2=144
v=12 m/s(i)


The light ray from the ball is travelling from the rarer medium to denser medium.

Let the distance appears to fish is xapp=v and real distance is xreal=h=u

Thus, μ2μ1=vu=xappxreal

μ21=xappxreal
or xapp=μ2xreal

Differentiate both sides.
dxappdt=μ2dxrealdt

By using equation (i),
vapp=μ2×v
or, vapp=43×12=16 m/s

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