The critical angle is the angle of incidence at which a light ray traveling from a denser medium to a less dense medium will be refracted along the interface between the two media instead of being transmitted. The Brewster angle is the angle of incidence at which a light ray traveling from a medium will be polarized parallel to the interface between the two media.
The critical angle and Brewster angle are related mathematically through Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction of the two media. The Brewster angle is equal to the arctangent of the index of refraction of the less dense medium over the index of refraction of the denser medium.
The critical angle and Brewster angle have practical applications in optics, specifically in the design of optical components such as lenses, prisms, and mirrors. They also have significance in understanding the polarization of light and the behavior of light at interfaces between different media.
The critical angle and Brewster angle are affected by the indices of refraction of the two media, the wavelength of the incident light, and the polarization state of the incident light. They can also be affected by the roughness or irregularities of the interface between the two media.
The critical angle and Brewster angle can be experimentally determined by measuring the angle of incidence at which total internal reflection occurs for the critical angle, and by using a polarizer to measure the angle of incidence at which the reflected light is completely polarized for the Brewster angle.