How to use it
- Type the Index of refraction of the first medium, for example 1.00 for air.
- Type the Index of refraction of the second medium, for example 1.50 for glass.
- Type the Angle of incidence, degrees, measured from the normal.
- Read the Angle of refraction and the speeds of light, then the steps.
Snell's law
When light passes from one transparent medium into another, it changes direction. Snell's law gives the new direction: the index of refraction times the sine of the angle is the same on both sides of the boundary (OpenStax, University Physics Volume 3, chapter 1).
n1 sin θ1 = n2 sin θ2
n = index of refraction, n = c ÷ v
θ1 = angle of incidence, from the normal
θ2 = angle of refraction, from the normal
c = 299 792 458 m/s, the speed of light in vacuum (exact)
v = the speed of light in the medium- Light entering a medium with a larger index bends toward the normal; leaving one for a smaller index it bends away from the normal.
- A ray that crosses a boundary between two identical media does not bend.
- The index depends on the wavelength, which is why refraction separates the colours of white light in a rainbow.
Critical angle and total internal reflection
When light goes from a medium with a larger index (n1 > n2) into one with a smaller index, the sine of the refraction angle grows faster than the sine of the incidence angle. It reaches 1 at the critical angle, sin θc = n2 ÷ n1. Beyond that angle no refracted ray exists and the light is totally reflected inside the first medium (OpenStax, same chapter).
What this calculator does not include
- The share of light that is reflected at the surface, and how it is polarised (the Fresnel equations).
- Media that absorb the light, which change its brightness as it travels.
- Several boundaries in a row with a thin layer between them, such as a film or a lens coating.
Worked example: from air into glass at 30°
With n1 = 1.00 and n2 = 1.50, the sine of the refraction angle is 1.00 × sin 30° ÷ 1.50 = 0.5 ÷ 1.5 = 0.3333, so θ2 = arcsin(0.3333) = 19.47°. The critical angle for light going back from glass to air is arcsin(1 ÷ 1.5) = 41.81°.
| Quantity | Value |
|---|---|
| Angle of refraction, air to glass at 30° | 19.47° |
| Speed of light in glass | 199,861,639 m/s |
| Critical angle, glass to air | 41.81° |
Frequently asked questions
What is the index of refraction?
The index n = c ÷ v is the speed of light in vacuum divided by its speed in the medium. Vacuum has n = 1, and most transparent materials have an index above 1.
Why is the angle measured from the normal?
Snell's law is written for angles from the normal, the line perpendicular to the surface. An angle measured from the surface itself gives a wrong sine, so the result would be wrong.
Why is there no refracted ray for my angle?
The light goes from a medium with a larger index into a smaller one, and the angle is above the critical angle. Then the sine of the refraction angle would exceed 1, so the light is totally reflected.
Can I use the calculator for light in water?
Yes. Enter the index of water from your textbook as one of the indices, with the index of the other medium, and the same method applies.
Is my data sent to a server?
No. The calculation runs in your browser, and nothing you type is sent to us or stored.
Sources
- OpenStax University Physics Volume 3, chapter 1 key equations: index of refraction n = c/v, law of refraction, critical angle
- NIST: speed of light in vacuum c, CODATA 2022 (299 792 458 m/s, exact)
Figures and text last checked on Tuesday, November 10, 2026.