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:

θi = arcsin[ sin( θr ) × nr ÷ ni ]


θr = the angle of refraction
θi = the angle of incidence
ni = the refraction idex of medium containing the incident ray
nr = the refraction idex of medium containing the transmitted ray

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

θi = arcsin[ sin( 90 ) × nr ÷ ni ]

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

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