Snell's Law Refraction Calculator
When light crosses the boundary between two transparent media it bends. Snell's law gives the angle of refraction from the angle of incidence and the two refractive indices: n1 * sin(theta1) = n2 * sin(theta2). Enter the index of the first medium, the angle of incidence in degrees, and the index of the second medium to find the refraction angle. When light moves to a less dense medium beyond the critical angle, the calculator reports total internal reflection and shows the critical angle.
Snell's law formula
n1 * sin(theta1) = n2 * sin(theta2)
theta2 = arcsin( (n1 / n2) * sin(theta1) )
Critical angle theta_c = arcsin(n2 / n1), only when n1 > n2
Total internal reflection when (n1 / n2) * sin(theta1) > 1
The refractive index measures how much a medium slows light relative to a vacuum. Light bends toward the normal when entering a denser medium and away from the normal when entering a less dense one.
Worked example
Light travels from water (n1 = 1.33) into air (n2 = 1) at an incidence angle of 30 degrees. sin(theta2) = (1.33 / 1) * sin(30) = 1.33 * 0.5 = 0.665, so theta2 = arcsin(0.665) = 41.68 degrees. The light bends away from the normal. The critical angle for this pair is arcsin(1 / 1.33) = 48.75 degrees, so 30 degrees refracts normally.
Snell's law: frequently asked questions
What is Snell's law?
Snell's law relates the angles of incidence and refraction at the boundary between two media: n1 * sin(theta1) = n2 * sin(theta2). The refractive indices n1 and n2 describe how much each medium slows light.
What are typical refractive indices?
The refractive index of a vacuum is exactly 1, air is about 1.0003, water is about 1.33, and common crown glass is about 1.52. The index fields here are editable so you can enter values for your specific media.
What is total internal reflection?
When light travels from a denser to a less dense medium (n1 greater than n2) and the incidence angle exceeds the critical angle, no refraction occurs and all light reflects internally. This calculator flags total internal reflection when sin(theta2) would exceed 1.
What is the critical angle?
The critical angle is the incidence angle at which the refracted ray travels along the boundary (theta2 equals 90 degrees). It is given by theta_c = arcsin(n2 / n1) and only exists when n1 is greater than n2.
Sources
- NIST: SI units (radian, degree).
- Snell's law is a standard result of geometrical optics. Refractive index defaults are textbook nominal values, editable for your media.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.