Snell's Law Calculator: Refraction Angle and Critical Angle
Pick the two materials, or enter your own refractive indices, and the angle at which the ray hits the boundary. The calculator tells you whether the ray refracts or is totally reflected.
Updated
Report a problem
Formula
- Snell's law:
n1 × sin(θ1) = n2 × sin(θ2), angles from the normal. - Refraction angle:
θ2 = asin(n1 × sin(θ1) ÷ n2), valid when the value inside asin is at most 1. - Critical angle (only when
n1 > n2):θc = asin(n2 ÷ n1). Ifθ1 > θcthe ray is totally internally reflected and leaves at angleθ1back in the first material. - Speed of light in a material:
v = c ÷ n,c = 299 792 458 m/s.
Preset indices are typical values at 589 nm: vacuum 1, air 1.000293, ice 1.31, water 1.333, ethanol 1.361, acrylic 1.491, crown glass 1.52, flint glass 1.62, diamond 2.417.
Worked example
Light in air hits water at 30°.
sin θ2 = 1.000293 × sin 30° ÷ 1.333 = 1.000293 × 0.5 ÷ 1.333 = 0.37522, so θ2 = 22.04°.
Going the other way, from crown glass to vacuum, θc = asin(1 ÷ 1.52) = 41.14°; at 30° the ray still escapes, refracting to 49.46°.
Frequently asked questions
What is Snell's law?
n1 × sin θ1 = n2 × sin θ2, with angles measured from the normal (the line perpendicular to the surface). Light from air (n = 1.000293) into water (n = 1.333) at 30° gives sin θ2 = 1.000293 × 0.5 ÷ 1.333 = 0.3752, so θ2 = 22.04°.
What is the critical angle?
When light goes from a denser to a less dense material, the critical angle is θc = asin(n2 ÷ n1). For crown glass (1.52) to vacuum it is asin(1 ÷ 1.52) = 41.14°. Beyond that angle nothing is transmitted.
When does total internal reflection happen?
Only when n1 is larger than n2 and the angle of incidence is greater than the critical angle. Water to vacuum has θc = 48.61°, so a ray at 60° is reflected completely. Optical fibres and diamonds rely on this.
Which way does the ray bend?
Into a higher index it bends toward the normal (a smaller angle), and into a lower index it bends away from it. Water to crown glass at 45° bends to 38.32°.
Are the refractive indices exact?
They are typical values for yellow light (589 nm) at room temperature. Real glass varies with its type, and the index changes slightly with colour, which is why a prism splits white light. Use the custom field for a measured value.