Critical Angle (Total Internal Reflection) Calculator
Compute the critical angle of incidence at which light traveling from a denser medium into a rarer one undergoes total internal reflection.
Beyond this incidence angle, light is totally internally reflected.
- 1
Index ratio n2 ÷ n1
1 ÷ 1.5 = 0.666667Must be less than 1 for total internal reflection to occur. - 2
Arcsin of ratio (radians)
arcsin(0.666667) = 0.729728 rad - 3
Convert to degrees
0.729728 × 180 ÷ π = 41.81°
How does this calculator work?
The critical angle is θc = arcsin(n2/n1), where n1 is the denser medium and n2 the rarer one. Above this angle of incidence, light is totally internally reflected instead of refracting out. It exists only when n1 > n2; for glass (1.50) to air (1.00) it is about 41.8 degrees.
Formula
How this is calculated
Enter the refractive index of the denser medium (n1), where the light is traveling, and the refractive index of the less-dense medium (n2) it is trying to enter. Both indices are dimensionless and must be at least 1 for ordinary materials (for example, 1.50 for crown glass, 1.33 for water, 1.00 for air).
The critical angle is found from Snell's law by setting the refraction angle to 90°: sin(θc) = n2 / n1, so θc = arcsin(n2 / n1), converted from radians to degrees. At incidence angles greater than θc the light cannot refract across the boundary and is entirely reflected back into the denser medium — the principle behind optical fibers, prisms, and gemstone sparkle.
A critical angle exists only when n1 > n2 (the ratio n2/n1 is below 1). If n2/n1 ≥ 1, light is moving into an equally or more optically dense medium, the arcsine is undefined, and total internal reflection never occurs, so the calculator flags the result as invalid.
Frequently asked questions
Total internal reflection only happens when light goes from a denser (higher-index) medium to a rarer (lower-index) one. If n2 ≥ n1, the ratio n2/n1 is at least 1, arcsin is undefined, and there is no critical angle.
Using n1 = 1.50 (glass) and n2 = 1.00 (air), θc = arcsin(1.00/1.50) ≈ 41.8°. Any ray hitting the glass-air boundary at more than about 41.8° from the normal is totally internally reflected.
Optical fibers are designed so that light rays strike the core-cladding boundary above the critical angle, trapping the signal inside the core by repeated total internal reflection with almost no loss.
Also known as
TG we-Calculate Editorial Team. (2026). Critical Angle (Total Internal Reflection) Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/critical-angle-calculator
TG we-Calculate Editorial Team. "Critical Angle (Total Internal Reflection) Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/critical-angle-calculator.
TG we-Calculate Editorial Team, "Critical Angle (Total Internal Reflection) Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/critical-angle-calculator
@misc{wecalculate_critical_angle_calculator, title = {Critical Angle (Total Internal Reflection) Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/critical-angle-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?