Final answer:
The apparent distance of the fish as observed by the bird is x + y/n, where x is the height of the bird above water, y is the depth of the fish below the surface, and n is the refractive index of water with respect to air.
Step-by-step explanation:
The question is about the optical phenomenon of refraction of light as it passes from air to water, which affects how a fish is perceived in water by a bird flying above. When light passes from a medium with a lower refractive index (like air) to a medium with a higher refractive index (like water), its speed decreases and it bends towards the normal line that's perpendicular to the interface of the two media.
According to Snell's law, the amount by which the light bends depends on the refractive indices of the two media and the angle of incidence. The observed distance is not the actual straight-line distance because of this bending of light. So if x is the height of the bird above the surface of the water, y is the depth of the fish below the surface, and n is the refractive index of water with respect to air, then the apparent distance of the fish as observed by the bird due to refraction would be given by x + y/n.
This solution uses the principle that a fish appears at a fraction of the real depth when viewed from above, as the light coming from the fish to the bird bends at the water surface due to refraction.