Angle of Refraction Calculator
Enter the incident angle and the refractive indices of both media to find the angle of refraction using Snell's law. Free browser tool gives instant results.
Snell's Law and Refraction
When light crosses a boundary between two media, it changes direction. The refracted angle depends on the incident angle and each medium's refractive index.
Snell's Law Formula
$$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$Rearranged for the refracted angle:
$$\theta_2 = \arcsin\left(\frac{n_1}{n_2}\sin(\theta_1)\right)$$If $\frac{n_1}{n_2}\sin(\theta_1) > 1$, total internal reflection occurs and no refracted ray exists. See also the Snell's Law Calculator.
Frequently Asked Questions
What is the refractive index?
It measures how much light slows in a medium compared to vacuum. Air is about 1.0003, water about 1.333, and crown glass about 1.52.
When does total internal reflection happen?
It occurs when light travels from a denser to a less dense medium and the incident angle exceeds the critical angle.
What is a typical air-to-water example?
For air ($n_1 \approx 1$) into water ($n_2 = 1.333$) at 45° incidence, the refracted angle is about 32°.
Are angles measured from the normal?
Yes. Both incident and refracted angles are measured from the surface normal, not from the surface itself.
Related Tools
FIRE Calculator
Boost Horsepower Calculator
Remove Comments
CSV to SQL Converter
Data URI Generator
Solar Farm Profit Calculator
Ares to Cents Converter
Future Value of Growing Annuity Calculator
Levy C Curve Generator
Root Mean Square Calculator
Inflation Calculator
Calorimetry Calculator
Modular Multiplicative Inverse Calculator
Maturity Value Calculator
Markdown Table Generator
Stone Calculator
Month Counter Calculator
Degree of Unsaturation Calculator
Generate Random Unix Time
Working Days