An archerfish swimming just below the surface of the water eyes an insect sittin

Question

An archerfish swimming just below the surface of the water eyes an insect sitting on a branch 1 m above the water's surface. The horizontal distance between the fish's eyes and the insect is also 1 m. You may neglect the distance between the eye and the surface. A Calculate the apparent angle at which the image of the insect appears to the fish, relative to vertical. B The archerfish can estimate the distance to the insect through parallax. Suppose that another insect lies directly above the fish, 1 m from the water's surface. Assuming that the fish's eyes are 6 mm apart, calculate the apparent distance to the fish if the archerfish didn't correct for refraction effects. You may assume that the fish is looking head-on at the insect.

Explanation / Answer

A:

The apparent heitght above the water is equal to the product of the refractive index of the water(4/3) and the actual height. Therefore, apparent heitght=4/3m; however the horixontal distance will be apparant as the actual horizontal distance . Thus the angle apparant to the fish is =tan-1(4/3)=530.

B:

If the fish is directly above the water surface, still the apparent distance would be 4/3m as due to parallax vision the rays entering the fish's eyes would not be normal to the surface of the water. Hence the apparent distance will be = 1.33m.

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