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A fish looking up through the water sees the outside 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

1. 36/√7
2. 36√7
3. 4√5
4. 36√5

Correct answer: 36/√7

Solution

Critical angle: sin(theta_c)=1/n=3/4, so tan(theta_c)=3/sqrt(7). Radius r = h*tan(theta_c) = 12*3/sqrt(7) = 36/sqrt(7) cm.

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