Critical Angle Calculator
Enter the refractive index of the denser medium (n1) and the rarer medium (n2) to find the critical angle for total internal reflection, in degrees and radians.
How to find the critical angle
- Enter n1, the refractive index of the denser medium the light starts in.
- Enter n2, the refractive index of the rarer medium it tries to enter.
- Read the critical angle in degrees and radians (requires n1 greater than n2).
Examples
Glass to air
n1 = 1.5 (glass), n2 = 1.0 (air)
critical angle = 41.8103 deg
Water to air
n1 = 1.33 (water), n2 = 1.0 (air)
critical angle = 48.7535 deg
Frequently asked questions
What is the critical angle?
It is the angle of incidence above which light cannot pass into a rarer medium and is instead totally internally reflected. It equals asin(n2 / n1).
Why must n1 be greater than n2?
Total internal reflection only happens when light travels from a denser medium to a rarer one. If n1 is not greater than n2, no critical angle exists.
What is total internal reflection?
When the angle of incidence exceeds the critical angle, all the light reflects back into the denser medium instead of refracting out. Optical fibers rely on this.
What units does the calculator return?
It returns the critical angle in both degrees and radians so you can use it directly in either system.
What are typical refractive indices?
Air is about 1.00, water about 1.33, and common glass about 1.50. Diamond is about 2.42, which gives a small critical angle and strong sparkle.
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