At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?

Light waves vibrate in many directions, but when these waves are aligned so that they vibrate in a single plane, we say the light is polarized. Polarization often occurs during the reflection of light, where certain angles cause light to become polarized – think of the glare you see on water or glass when the sun is at a certain position in the sky. It is this principle that polarized sunglasses use to reduce glare; they filter out light waves that aren't vibrating in the desired plane, improving visual comfort and visibility.

Polarization is not just a neat trick for sunglasses; it has important applications in photography, LCD technology, and even in scientific research, where analyzing the polarization of light can reveal properties of materials and phenomena that are otherwise invisible to the naked eye.

Think of the refractive index as a measure of how much a material can bend light. It is a dimensionless number that indicates the degree to which light slows down when it enters a material from a vacuum (or air, for most practical purposes, as its refractive index is close to 1). Substances with a higher refractive index bend light more than those with a lower index.

The refractive index is crucial in determining how light interacts at the boundary of two different media, like air and water or air and glass. It's responsible for the bending of a straw's image in a glass of water, the focusing power of lenses in glasses, and is a fundamental concept in understanding phenomena such as mirages, rainbows, and optical fibers.

The angle of incidence is the angle that an incoming wave, like a beam of light, makes with a perpendicular line to the surface it hits, known as the normal. It's a vital concept when studying how light reflects off surfaces and determines the behavior of the light wave—whether it will be absorbed, reflected, or refracted.

The angle of incidence not only affects the polarization of light, as described by Brewster's Law, but also plays a key role in other optical phenomena. For example, when considering the breathtaking patterns of colors in a soap bubble, it's the variations in the angle of incidence across the curved surface that contribute to the display of different colors.