A fish under water is viewing obliquely a fisherman standing on the bank of a lake. Does the man look taller or shorter than what he is actually?
Answer (2)
The fisherman appears shorter to the fish due to light refraction as it moves from water to air. This bending of light alters the perceived dimensions of objects. Therefore, the fish will see the fisherman as shorter than he really is.
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When a fish underwater is looking at a fisherman standing on the bank of a lake, it perceives the fisherman's image through refraction. Refraction is the bending of light as it passes from one medium to another with a different density, in this case, from water to air.
Here's how it works step-by-step:
Light Behavior: Light travels more slowly in water than in air due to the higher density of water. This change in speed causes the light rays to bend at the surface of the water.
Law of Refraction: According to Snell's Law, which governs refraction, the angle of incidence (the angle the light ray makes with the normal in water) is greater than the angle of refraction (the angle the light ray makes with the normal in air). Mathematically, this is expressed as:
n 1 sin ( θ 1 ) = n 2 sin ( θ 2 )
where n 1 and n 2 are the refractive indices of water and air, respectively, and θ 1 and θ 2 are the angles of incidence and refraction.
Perception: This bending makes objects appear closer to the surface than they actually are, creating a distorted image for the fish.
Apparent Height: Consequently, the fisherman appears shorter than his actual height to the fish. This is because the light paths are bent, compressing the vertical scale of the fisherman's image.
Therefore, due to refraction, the fish sees the fisherman as shorter than he really is.
