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Chapter 9: Problem 29

One sometimes hears the expression, "It was like shooting fish in barrel!" This usually is taken to mean that the task, whatever it was, was easy to complete. But is it really easy to shoot fish in a barrel? Only if you know some optics! Suppose you're in a boat and spy large fish a few meters away. If you want to shoot the fish, how should you aim? Above the image of the fish? Below it? Directly at the image? Explain your choice. (You may assume that the path of the projectile you fire will not be deviated from a straight line upon entering the water, unlike light.

Short Answer

Expert verified
Answer: To account for the optical refraction, one should aim slightly below the apparent image of the fish, as the fish appears to be shallower than its actual position due to the refraction of light.

Step by step solution

01

Understand the principle of refraction

Refraction occurs when light waves pass between different media, like air and water, causing the light to change direction. In this case, we should consider the refraction of light from the water surface to understand where the fish appears to be.
02

Snell's Law

Snell's Law describes the relationship between the angles of incidence and refraction for a wave passing through different media. It states that: n1 * sin(θ1) = n2 * sin(θ2) where n1 and n2 are the refractive indices of the first and second media (air and water, respectively), and θ1 and θ2 are the angles of incidence and refraction, respectively.
03

Consider the case of shooting fish

Since light travels faster in air than in water, when light enters the water, it bends towards the normal (the line perpendicular to the surface). This causes the angle of refraction in water (θ2) to be smaller than the angle of incidence in air (θ1). It means the fish's image appears to be closer to the surface than its actual position. In other words, we see the fish in a shallower position due to the refraction of light.
04

Determine where to aim

Knowing that the fish's image appears to be shallower than its actual position, to shoot the fish, we should aim slightly below the apparent image of the fish. This way, when the projectile enters the water, it will be heading towards the actual location of the fish rather than the refracted image.

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