Math
Snell's Law Calculator
Apply n1 * sin(theta1) = n2 * sin(theta2). Solve for refraction angle, incidence angle, or refractive index. Detects total internal reflection and critical angle.
Snell's Law Calculator
Given both indices and the incidence angle, solve theta2 = arcsin((n1/n2) * sin(theta1)).
Index of the medium the light starts in. Must be greater than zero.
Index of the medium the light enters. Must be greater than zero.
Angle measured from the surface normal in medium 1. Range 0 to 90 degrees.
Refraction angle
22.036902 deg
n1
1.000293
n2
1.333
Incidence angle
30 deg
Refraction angle
22.036902 deg
Critical angle
n/a (n1 <= n2)
Wave speed ratio v2/v1
0.750407
Frequently Asked Questions about the Snell's Law Calculator
What is Snell's Law?
Snell's Law relates the angles of incidence and refraction when a light ray passes between two media: n1 x sin(theta1) = n2 x sin(theta2). Here n1 and n2 are the refractive indices of the two media, theta1 is the angle of incidence measured from the surface normal, and theta2 is the angle of refraction. The law follows from Fermat's principle and from the fact that wave speed in a medium equals c / n.
How do I find the angle of refraction?
Rearrange Snell's Law: sin(theta2) = (n1 / n2) x sin(theta1), then take the inverse sine. For light going from air (n1 = 1.000293) into water (n2 = 1.333) at theta1 = 30 degrees: sin(theta2) = (1 / 1.333) x 0.5 = 0.3751, so theta2 = arcsin(0.3751) which is about 22.03 degrees.
What is the critical angle and total internal reflection?
The critical angle is the incidence angle at which the refracted ray would graze along the surface (theta2 = 90 degrees). It exists only when light travels from a denser medium into a less dense one (n1 > n2). Its value is theta_c = arcsin(n2 / n1). Beyond this angle no refracted ray exists and all the light bounces back into medium 1, which is called total internal reflection. For water to air the critical angle is about 48.61 degrees.
What are typical refractive indices?
Common indices at visible-light wavelengths: vacuum 1.000, air 1.000293 (close enough to 1 for most problems), water 1.333, crown glass 1.52, flint glass 1.62, and diamond 2.42. Higher index means light travels slower in that medium and bends more sharply toward the normal when entering. The presets in this calculator load these values for you.
How does Snell's Law relate to the speed of light?
Refractive index is defined as n = c / v, where c is the speed of light in vacuum and v is its speed in the medium. Substituting into Snell's Law gives sin(theta1) / sin(theta2) = v1 / v2 = n2 / n1. So the wave-speed ratio v2 / v1 equals n1 / n2, which this calculator reports alongside the angle result.