What is the critical angle?

The critical angle is a concept in optics that refers to the angle of incidence at which light, or any other electromagnetic wave, is refracted (bent) at an angle of 90 degrees or becomes parallel to the boundary between two different optical media, typically from a denser medium to a less dense one. When the angle of incidence exceeds the critical angle, instead of refracting into the second medium, the light is internally reflected within the first medium.

The critical angle is a result of Snell's Law, which relates the angles of incidence and refraction when light passes through the boundary between two different materials with different refractive indices. The formula for Snell's Law is:

n1 * sin(θ1) = n2 * sin(θ2)

Where:

n1 and n2 are the refractive indices of the first and second media, respectively.
θ1 is the angle of incidence.
θ2 is the angle of refraction.
When the angle of incidence (θ1) reaches a critical value (the critical angle, θc), the angle of refraction (θ2) becomes 90 degrees, and sin(θ2) becomes 1. In this case, the equation becomes:

n1 * sin(θc) = n2 * 1

So, the critical angle (θc) can be calculated as:

θc = arcsin(n2 / n1)

The critical angle is an important concept in various optical applications, such as total internal reflection in fiber optics, the operation of prisms, and understanding the behavior of light at the boundary between different optical materials.