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Question

A point source of light is placed at the bottom of the water lake. If the area of the illuminated circle on the surface is equal to 3 times the square of the depth of the lake. The refractive index of water is :

A
π3+1
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B
π3+1
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C
π3+1
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D
π4+1
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Solution

The correct option is A π3+1
Light of the source emerges out of water only when the incident angle at the water air boundary equals critical angle. (θc)

Let depth of lake =H

and radius of Illuminated circle =R

Given : πR2=3H2

H2=π3R2 ...(1)

From figure,

sinθc=RR2+H2

also we know, sinθc=(1μ) [μ: Refractive index of water]

So we get, from above:-

μ=R2+H2R=R1+π3R [from (1)]

μ=1+π3

1061121_1163147_ans_0fb7498fc2934fb991ed09443dbbac21.png

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