Critical Angle

in optics, the angle of incidence between a light ray and an interface above which the ray reflects completely instead of passing through the interface from one medium to the other. The complete reflection of the light ray is referred to as total internal reflection.

The critical angle is a function of the index of refraction of the two media.

With the Snell's Law equation solved for the angle of incidence:

θ_i = arcsin[ sin( θ_r ) × n_r ÷ n_i ]

Where:

θ_r = the angle of refraction
θ_i = the angle of incidence
n_i = the refraction idex of medium containing the incident ray
n_r = the refraction idex of medium containing the transmitted ray

The critical angle is the value for θ_i at which θ_r equals 90 degrees (1.57 radians):

θ_i = arcsin[ sin( 90 ) × n_r ÷ n_i ]

Total internal reflection occurs when the θ_r exceeds 90 degrees (1.57 radians).