Light travels in a medium with index n1 toward a boundary...

Light travels in a medium with index $n_{1}$ toward a boundary with another material of index $n_{2}<n_{1}$. (a) Which is larger, the critical angle or Brewster's angle? Does the answer depend on the values of $n_{1}$ and $n_{2}$ (other than assuming $n_{2}<n_{1}$ )? (b) What can you say about the critical angle and Brewster's angle for light coming the other way (from the medium with index $n_{2}$ toward the medium with $n_{1}$ )?

Light travels in a medium with index $n_{1}$ toward a boundary with another material of index $n_{2}<n_{1}$.
(a) Which is larger, the critical angle or Brewster's angle? Does the answer depend on the values of $n_{1}$ and $n_{2}$ (other than assuming $n_{2}<n_{1}$ )? (b) What can you say
about the critical angle and Brewster's angle for light coming the other way (from the medium with index $n_{2}$ toward the medium with $n_{1}$ )?

Key Concepts

Index of Refraction

This concept describes how fast light travels through a medium compared to vacuum. It is a fundamental property that determines how light bends when it crosses from one medium to another and is crucial to understanding the phenomena of refraction, critical angle, and Brewster's angle.

Snell's Law

Snell's Law relates the angles of incidence and refraction to the indices of refraction of the two media. It provides the mathematical framework for predicting how light will bend at the boundary between different media and is key to deriving both the critical angle and Brewster's angle.

Critical Angle

The critical angle is the minimum angle of incidence in the denser medium at which light is totally internally reflected rather than refracted into the rarer medium. It is derived from Snell's Law and occurs only when light travels from a medium of higher index to one of lower index.

Brewster's Angle

Brewster's angle is the angle of incidence at which light with a particular polarization (p-polarized light) is not reflected at all, but entirely refracted. This occurs because the reflected and refracted rays are perpendicular at this angle, leading to complete polarization of the reflected light.

Polarization

Polarization refers to the orientation of the oscillations of the electric field in a light wave. The concept is connected to Brewster's angle, as the light reflected at this angle is completely polarized, making it an important aspect of understanding light behavior at interfaces.

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