A fish in a lake is at a 6.3 m distance from the edge of the lake. If it is just able to see a tree on the edge of the lake, its depth in the lake is m. The refractive index of the water is 1.33.

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Accepted Answer

(1) 5.52. Given: the fish is 6.3 m from the edge horizontally, n=1.33, and the tree is only just visible. Idea: 'just able to see' means the light from the tree skims into the water along the surface and travels on to the fish at the critical angle — the rim of the circular window a fish sees the world through. sin C=1/n=1/(1.33)=0.752, so C=48.8°. That ray makes the angle C with the vertical, so tan C=x/h with x the horizontal distance and h the depth. h=(6.3)/(tan 48.8°)=(6.3)/(1.140)=5.52 m Anything outside that cone is hidden from the fish by total internal reflection.

A fish in a lake is at a 6.3 m distance from the edge of the lake. If it is just able to see a tree on the edge of the lake, its depth in the lake is ________ m. The refractive index of the water is 1.33.

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