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Question

A disc is placed on the surface of a pond filled with liquid of refractive index 53. A source of light is placed 4 m below the surface of the liquid. The minimum area of the disc so that light does not come out of the liquid into air is about

A
28.26m2
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B
26.28m2
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C
28.26cm2
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D
26.28cm2
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Solution

The correct option is A 28.26m2
Let radius of the disc be r.
Distance of source of light from the surface of liquid = AO = h = 4 m
Refractive index, μ=53
Light does not come out of the liquid into the air if:
sin c=1μ [c = critical angle]
rAB=1μ [InΔAOB,sinc=OBAB=rAB]
rr2+h2=1(53) [AB=OB2+AO2=r2+h2]
rr2+42=35
r=3m
Area of the disc=πr2
=3.14×3×3
=28.26m2
Hence, the correct answer is option (a).

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