The back wall of a home aquarium is a mirror that is a...

The back wall of a home aquarium is a mirror that is a distance of $40.0 \mathrm{~cm}$ away from the front wall. The walls of the tank are negligibly thin. A fish, swimming midway between the front and back walls, is being viewed by a person looking through the front wall. The index of refraction of air is $n_{\text {air }}=1.000$ and that of water is $n_{\text {water }}=1.333 .$ (a) Calculate the apparent distance between the fish and the front wall. (b) Calculate the apparent distance between the image of the fish and the front wall.

Key Concepts

Snell's Law

Snell's Law is the fundamental principle that relates the angles of incidence and refraction when light passes between two media with different indices of refraction. It explains how and why light bends at the interface between two substances, which is essential for understanding the apparent displacement of objects viewed across media boundaries. This law provides the mathematical basis for determining the change in direction of light rays as they pass from water to air.

Index of Refraction

The index of refraction is a measure of how much a medium slows down light compared to its speed in a vacuum. It determines the degree to which light bends when entering or leaving the medium according to Snell's Law. Different media have different indices of refraction, and this difference leads to phenomena such as the apparent depth effect when observing objects underwater from air.

Apparent Depth

Apparent depth refers to the phenomenon where objects submerged in a medium like water appear closer to the surface than they actually are when viewed from another medium, such as air. This occurs due to the refraction of light, which alters the perceived position of the object. The apparent depth is typically calculated by scaling the true depth by the ratio of the indices of refraction of the two media involved.

Plane Mirror Image Formation

Plane mirror image formation describes how a flat reflective surface creates a virtual image that is laterally inverted and appears to be as far behind the mirror as the object is in front. This concept is essential in understanding how images are formed by reflective surfaces, and when combined with refraction phenomena, it provides the basis for determining the apparent location of images in environments where reflections and medium transitions occur.

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