A fish looking upwards through the water seeing 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

Step-by-step solution

For total internal reflection, μ = 1 sin θ C ⇒ sin θ C = 1 μ = 3 4 ∴ tan θ C = sin θ C 1 - sin 2 θ C = 3 / 4 1 - 9 16 = 3 4 × 4 7 = 3 7 ∴ R 12 = 3 7 ⇒ R = 36 7 cm .