Review Conceptual Example 4 as background for this problem....

Review Conceptual Example 4 as background for this problem. A man in a boat is looking straight down at a fish in the water directly beneath him. The fish is looking straight up at the man. They are equidistant from the air-water interface. To the man, the fish ap pears to be $2.0 \mathrm{~m}$ beneath his eyes. To the fish, how far above its eyes does the man appear to be?

Key Concepts

Refraction

Refraction is the bending of light as it passes from one medium to another due to a change in its speed. This phenomenon is described by Snell’s law, and it causes the apparent position of objects to shift when viewed from one medium into another. In many scenarios, such as viewing objects underwater from above or vice?versa, refraction alters the perceived depth or height of these objects relative to their actual, physical positions.

Snell's Law

Snell’s law is the fundamental law that governs the refraction of light at the interface between two media with different indices of refraction. It relates the sine of the angle of incidence to the sine of the angle of refraction with the refractive indices of the two media. This law is key in determining how light rays bend at boundaries, hence affecting the apparent positions of objects when seen across media boundaries.

Apparent Depth

The concept of apparent depth refers to the observation that objects submerged in a medium (like water) appear closer to the interface than they really are when viewed from another medium (like air). This is a direct consequence of refraction; for example, objects under water seem more shallow to an observer above water. Conversely, the same optical principles can alter the perceived height (or distance above the water) of objects viewed from underwater, making them appear at a different position than their true location.

Reversibility of Light

The reversibility of light means that light rays follow the same path when the direction of travel is reversed. This principle is crucial when analyzing situations where two observers in different media look at each other through a refractive interface. It allows one to apply the same optical laws to determine the apparent position of one observer as seen by the other, thereby linking the apparent depth (or height) effects on both sides of the interface.

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