Critical Angle Calculator

How it is calculated

The critical angle follows from Snell's law with the refracted ray running along the boundary (90 degrees): θc = arcsin(n2 / n1). Here n1 is the refractive index of the denser medium the light starts in and n2 is the index of the less dense medium beyond the surface; both are unitless. The result is an angle of incidence in degrees, measured from the surface normal, and is rounded to two decimals. If you leave n2 empty (or enter zero or a negative number), the tool assumes air with n2 = 1.0. Total internal reflection only exists when n2 is smaller than n1, so if n2 is equal to or greater than n1 there is no critical angle and no result is shown.

Common mistakes

• Swapping the two indices: n1 must be the denser medium the light is in. Putting the air value in n1 and glass in n2 gives no result, because n2 is not smaller than n1.
• Measuring the angle from the surface instead of from the normal. The answer is the angle to the perpendicular line; the angle to the surface itself is 90° minus the result.
• Expecting an answer for light going from a less dense medium into a denser one, such as air into water. Total internal reflection cannot happen in that direction.
• Leaving n2 empty and forgetting that air (1.0) is then assumed; for glass-to-water or diamond-to-glass boundaries you must enter n2 yourself.