About the Snell's Law Calculator
This Snell's law calculator shows how light bends when it crosses from one material into another. Choose the two media from a list of common materials (air, water, glass, acrylic, diamond and more) or type your own refractive indices, enter the angle of incidence, and get the angle of refraction measured from the normal. You can also switch modes to find an unknown refractive index from two measured angles.
It suits physics and optics students, teachers preparing ray-diagram exercises, and anyone working with lenses, prisms, fibre optics or underwater cameras. The calculator also reports the critical angle for total internal reflection — the effect that traps light inside optical fibres and makes diamonds sparkle — and the speed of light in the second medium.
Angles are measured from the normal (the line perpendicular to the surface), not from the surface itself. Refractive indices vary slightly with wavelength; the listed values are typical figures for yellow sodium light around 589 nm (air at 0 °C and 1 atm; water and ethanol near room temperature). Real glasses vary by composition, so use a custom index from the manufacturer's datasheet for precise work.
How to use the snell's law calculator
- 1Choose whether to find the refraction angle or an unknown refractive index.
- 2Select the material the light starts in, and the material it enters.
- 3Enter the angle of incidence measured from the normal.
- 4Read the refraction angle, critical angle and what happens to the ray.
- 5Use the chart to see how the refracted angle changes with incidence.
Formula and method
Snell's law relates the angles a light ray makes with the normal on each side of a boundary to the refractive indices of the two materials. Solving for the refracted angle gives θ₂ = arcsin(n₁ sin θ₁ ÷ n₂); solving for an unknown index gives n₂ = n₁ sin θ₁ ÷ sin θ₂.
When light goes from a higher-index medium to a lower-index one, n₁ sin θ₁ ÷ n₂ can exceed 1. There is then no real refracted angle and all the light reflects back — total internal reflection. The threshold incidence angle is the critical angle θc = arcsin(n₂ ÷ n₁). The speed of light in a medium is c ÷ n, with c = 299,792,458 m/s.
- n₁, n₂
- Refractive indices of the incident and refracting media
- θ₁
- Angle of incidence from the normal
- θ₂
- Angle of refraction from the normal
- θc
- Critical angle for total internal reflection
- c
- Speed of light in a vacuum
Worked examples
Light from air into water at 30°
sin θ₂ = 1.000293 × sin 30° ÷ 1.333 = 0.3752, so θ₂ = 22.04°. The ray bends toward the normal because water is optically denser, and light slows to about 225,000 km/s.
Glass to air at 45° — total internal reflection
The critical angle is arcsin(1.000293 ÷ 1.5) = 41.83°. Since 45° is larger, n₁ sin θ₁ ÷ n₂ = 1.06 exceeds 1 and the light is totally reflected inside the glass.
Measuring an unknown index
A ray entering a block from air at 40° refracts to 25°. n₂ = 1.000293 × sin 40° ÷ sin 25° = 1.521, which matches crown glass. The ray is deviated by 15°.
Frequently asked questions
What is Snell's law?+
Snell's law states that n₁ sin θ₁ = n₂ sin θ₂: the product of refractive index and the sine of the angle from the normal is the same on both sides of a boundary between two transparent materials.
What is the critical angle?+
The critical angle is the incidence angle, inside the higher-index material, above which light cannot escape and is totally reflected. For glass (n = 1.5) to air it is about 41.8°, and for water to air about 48.6°.
Does light bend toward or away from the normal?+
Light bends toward the normal when it slows down entering a higher-index material (air to water) and away from the normal when it speeds up entering a lower-index material (water to air).
What is the refractive index of water and glass?+
At visible wavelengths water is about 1.333, common window and crown glass about 1.50–1.52, flint glass about 1.62, acrylic about 1.49 and diamond about 2.42. Air is about 1.0003.
Why are angles measured from the normal?+
Snell's law is written with angles measured from the normal, an imaginary line perpendicular to the surface. If you measured an angle from the surface, subtract it from 90° before using the calculator.