Snell's Law Refraction Calculator
Solve any refraction variable using indices or speeds, with signed ray directions.
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- Free preview: the rules, dates and checks that apply to your figures, with every computed amount hidden.
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| Quantity | Value |
|---|
Model assumptions
Reference refractive indices
Approximate values at 589 nm in vacuum. Air: 0 °C, 1 atm; water and solids: 20 °C. Enter your own verified values for other conditions.
| Medium | Index | Condition |
|---|---|---|
| Vacuum | 1 | exact definition |
| Air | 1.000293 | 0 °C, 1 atm |
| Fresh water | 1.333 | 20 °C |
| Crown glass | 1.52 | 20 °C reference sample |
| Diamond | 2.419 | 20 °C reference sample |
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Snell's Law Refraction Calculator
Solve an incident angle, transmitted angle, refractive index or scalar propagation speed at a flat interface. Angles are measured from the normal. Light mode also gives a critical angle when the propagation direction permits total internal reflection, a dielectric Brewster angle and the phase speed in each medium.
The free preview masks calculated values and shows a marked diagram preview. A Pro pass opens the complete values, ray drawing, copy and reports. The reference-index table is public and approximate; enter verified indices for your wavelength and material. The scalar-speed form can illustrate ultrasound or seismic refraction, with mode conversion and anisotropy excluded.
How to use it
- Choose refractive indices for light or propagation speeds for a scalar wave.
- Choose the one unknown; enter only the other three quantities.
- Measure angles from the interface normal and keep them between 0° and 90°.
- Calculate, inspect any total-internal-reflection result, and use the reference table only at its stated conditions.
Examples
n1 = 1.5, n2 = 1, incident angle 30°
Transmitted angle about 48.5904°; critical angle about 41.8103°
n1 = 1.5, n2 = 1, incident angle 50°
No propagating transmitted ray in this model
v1 = 1,500 m/s, v2 = 3,000 m/s, incident angle 30°
A grazing transmitted direction of 90°
Equations and diagram
Light obeys n1 sin(theta1) = n2 sin(theta2). The scalar-speed form is sin(theta1)/v1 = sin(theta2)/v2. For decreasing light index, the critical angle is asin(n2/n1). For light in nonabsorbing dielectrics, Brewster's angle is atan(n2/n1) and phase speed is c/n.
The ray drawing places the incident medium above the interface and the transmitted medium below it. Its arrows indicate travel directions. It shows a reflected direction without computing reflection intensity. At critical incidence, the transmitted ray grazes the interface; larger incidence has no propagating transmitted ray.
Reference-index conditions
The small table uses OpenStax's reference indices at a vacuum wavelength of 589 nm. Air is tabulated at 0 °C and 1 atm; fresh water and the listed solids at 20 °C. Real composition, dispersion, absorption and temperature change the index. Vacuum n = 1 is a definition.
Sources
See OpenStax: refraction, total internal reflection, polarization and Brewster's law, and reference refractive indices.
Limitations
- Only positive real indices and scalar speeds are supported; absorbing, anisotropic and metamaterial models are excluded.
- Solving an index from two zero angles is indeterminate, so the calculator asks for usable nonzero angles.
- Brewster's angle is specific to the light dielectric model; it is not reported for generic scalar waves.
- No ultrasound/seismic mode conversion, intensity coefficient or professional optical/geophysical design is supplied.
Privacy
On this device; its files download once
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot. PDF reports may load MySmartCoPilot font files; entered values stay on your device.
Frequently asked questions
What do I get without a pass?
Without a pass, Snell's Law Refraction Calculator shows the rules, dates and checks that apply to your figures, with every computed amount hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
Are angles measured from the surface?
No. Enter the angle from the perpendicular normal. A surface angle of 60° is a normal angle of 30°.
When does total internal reflection occur?
For light travelling toward a lower index, the transmitted-angle equation stops having a propagating solution above the critical angle. At the critical angle itself, the transmitted direction is grazing.
Can I use ultrasound or seismic speeds?
The scalar-speed equation is available as an ideal illustration. Real elastic waves can change modes and behave anisotropically; those effects need a more complete physical model.
Are the table indices universal constants?
No. They are approximate material values at stated conditions and a stated wavelength. Vacuum n = 1 is exact; the material entries are editable reference choices.