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Question

# A fish looking up through the water sees the outyside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface, the radius of this circle in cm is

A
367
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B
36/7
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C
36/5
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D
4/5
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Solution

## The correct option is B 36/√7The refractive index of water is N=43The critical angle is ic=sin−11n=sin−134if r is the radius of the circular horizon and h is the distance of the fish from the surface then from the geometry, cot ic=rhFrom trigonometry1+cot2ic=cosec2ic1+h2r2=1sin2ic1+h2r2=4232r=h√9√7=12×√97cm=36√7cm

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