Critical Angle Calculator Formula
Understand the math behind the critical angle calculator. Each variable explained with a worked example.
Formulas Used
Critical Angle
critical_angle = asin(n2 / n1) * 180 / piVariables
| Variable | Description | Default |
|---|---|---|
n1 | Denser Medium Refractive Index | 1.5 |
n2 | Less Dense Medium Refractive Index | 1 |
How It Works
Critical Angle
The critical angle is the angle of incidence above which total internal reflection occurs when light travels from a denser to a less dense medium.
Formula
theta_c = arcsin(n2 / n1)
where n1 > n2. Above this angle, no light passes through the boundary.
Worked Example
Light going from glass (n=1.5) to air (n=1).
- 01theta_c = arcsin(n2/n1)
- 02theta_c = arcsin(1/1.5)
- 03theta_c = arcsin(0.667)
- 04theta_c = 41.81°
Frequently Asked Questions
What is total internal reflection?
When light hits a boundary at an angle greater than the critical angle (going from denser to less dense medium), all light is reflected back with no transmission.
How do fiber optics work?
Light enters the fiber and hits the cladding boundary at angles exceeding the critical angle, so it bounces along the fiber with minimal loss.
Why do diamonds sparkle so much?
Diamond has a very high refractive index (2.42), giving a small critical angle (~24.4°). Light enters but undergoes many total internal reflections before exiting, creating brilliance.
Learn More
Guide
Understanding Optics and Lenses
A complete guide to optics and lenses. Learn about refraction, Snell's law, converging and diverging lenses, the thin lens equation, magnification, mirrors, and optical instruments.
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