A fish in a flat-sided aquarium sees a can of fish food on...

A fish in a flat-sided aquarium sees a can of fish food on the counter. To the fish's eye, the can looks to be $30 \mathrm{cm}$ outside the aquarium. What is the actual distance between the can and the aquarium? (You can ignore the thin glass wall of the aquarium.)

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Key Concepts

Snell's Law

Snell's Law is a fundamental principle in optics that relates the angles of incidence and refraction to the indices of refraction of two media. It explains how and why light rays bend when transitioning between materials of different optical densities. This principle is crucial for understanding phenomena such as the apparent displacement of objects when viewed through a medium like water.

Index of Refraction

The index of refraction is a measure of how much the speed of light is reduced in a particular medium compared to its speed in a vacuum. It is a key parameter in calculating how light bends when it passes between different media. The difference in the index of refraction between water and air is what causes the apparent depth of objects viewed from one medium to the other to differ from their actual depth.

Apparent Depth

Apparent depth refers to the phenomenon in which the perceived position of an object submerged in a medium such as water appears to be closer to the surface than it actually is. Due to the refraction of light at the interface between two media with different indices of refraction, the true position of the object is 'shifted' relative to its observed position. This concept is critical when solving problems that involve determining the real position of objects viewed from another medium.

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