Physics · Optics
Snell's law calculator.
Choose the two media, enter the angle of the incoming ray and see the angle it bends to, or whether it is totally reflected.
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Result
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Snell's law and the critical angle
Snell's law says n1 sin θ1 = n2 sin θ2, with both angles measured from the normal, the line perpendicular to the surface. Going into a higher index the ray bends toward the normal. When n2 is lower than n1 there is a critical angle θc = arcsin(n2 ÷ n1), the incident angle that makes the refracted ray graze the surface at 90°. Beyond it all the light reflects (OpenStax).
Worked example. Light in from vacuum (n = 1) onto crown glass (n = 1.52) at 30°: sin θ2 = sin 30° ÷ 1.52, so θ2 = 19.205°. Air to water (1.33) at 45° bends to 32.118°. Going the other way, from glass into air the critical angle is 41.14°, so a 50° ray is totally reflected. For diamond (2.417) into air it is only 24.44°.
The index of a material is n = c ÷ v, the ratio of the speed of light in a vacuum to the speed in the material, and is always at least 1. This is a classroom ray-optics model for a flat boundary and one colour of light. It is not for lens, fibre-optic or safety-critical optical design.
Refractive indices used in the presets
| Material | Index n |
|---|---|
| Vacuum | 1.0 |
| Air at STP | 1.00029 |
| Ice | 1.31 |
| Water at 20 °C | 1.33 |
| Ethyl alcohol | 1.36 |
| Fused quartz | 1.46 |
| Glycerine | 1.473 |
| Typical crown glass | 1.52 |
| Heavy flint glass | 1.65 |
| Sapphire | 1.77 |
| Diamond | 2.417 |
Values from the HyperPhysics index of refraction table. They are for visible light; n changes slightly with colour and temperature.
Frequently asked questions
What is Snell's law?
n1 × sin θ1 = n2 × sin θ2, where n is the refractive index of each medium and the angles are measured from the normal.
How do I find the critical angle?
θc = arcsin(n2 ÷ n1), only when n2 is less than n1. Glass (1.52) to air is 41.14°.
What happens above the critical angle?
All the light is reflected back into the first medium. This is total internal reflection and the calculator reports it instead of a refraction angle.
Why does light bend toward the normal in glass?
Light is slower in glass. Going from a lower index to a higher one makes the ray bend toward the normal.
Can I use my own refractive index?
Yes. Type any index of 1 or more into the n1 or n2 box.
Sources
Checked
- OpenStax University Physics Volume 3, 1.3 Refraction
- OpenStax University Physics Volume 3, 1.4 Total Internal Reflection
- OpenStax University Physics Volume 3, 1.1 The Propagation of Light
- HyperPhysics: Index of Refraction table
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Scope
Idealised ray-optics model. Not for lens, fibre-optic or safety-critical optical design. Results are arithmetic from the formulas shown, for study and general interest, and not professional or engineering advice.