Snell's law calculator
Pick the two media from the list or enter their refractive indices, then the angle you know. The calculator applies Snell's law, tells you when light is totally reflected instead of refracted, and shows the critical angle.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: the angle of refraction, the angle of incidence or n₂.
- Pick the first medium (where the light comes from) and the second medium, or enter custom indices.
- Enter the known angle or angles, measured from the normal.
- Read the result, the critical angle (when there is one) and how much the ray bends.
- Snell’s law: n₁ × sin θ₁ = n₂ × sin θ₂.
- Angle of refraction: θ₂ = arcsin(n₁ × sin θ₁ ÷ n₂); if the sine comes out above 1, the light is totally reflected.
- Unknown index: n₂ = n₁ × sin θ₁ ÷ sin θ₂.
- Critical angle: θc = arcsin(n₂ ÷ n₁) for n₁ > n₂.
Worked example
Light from air into water at 30°: sin θ₂ = 1.000293 × 0.5 ÷ 1.333 = 0.3752, so θ₂ = 22.04°. The ray bends 7.96° toward the normal.
The other way, from water into air at 60°: 1.333 × sin 60° ÷ 1.000293 = 1.154, more than 1, so there is total internal reflection. The critical angle is 48.63°.
Tips
- Angles from the normal, not the surface. A ray grazing the surface has an angle close to 90°.
- Faster medium, bigger angle. Going into a lower index, the ray bends away from the normal.
- Colour matters. Glass bends blue light a little more than red, which is why prisms split white light.
Frequently asked questions
What is Snell's law?
When light passes from one medium into another, n₁ × sin θ₁ = n₂ × sin θ₂, where n is the refractive index and the angles are measured from the normal, the line perpendicular to the surface.
What is total internal reflection?
When light goes from a denser medium into a less dense one (n₁ > n₂) at more than the critical angle, sin θ₂ would have to be above 1. No refracted ray exists and all the light reflects back, as in optical fibres.
How is the critical angle calculated?
θc = arcsin(n₂ ÷ n₁), only when n₁ > n₂. From water (1.333) into air it is about 48.6°, from crown glass (1.52) into air about 41.2°.
Which refractive indices are in the list?
Typical values for yellow light near room temperature, such as 1.333 for water and 2.417 for diamond. The index changes slightly with wavelength and temperature; choose Custom index to enter your own.