Calculates the angle light bends to as it passes from one transparent material into another with a different refractive index.
How it works
The first material’s refractive index and the sine of the incidence angle are combined and divided by the second material’s refractive index, then inverted with arcsine to find the refraction angle.
What this does not include
This does not include finding a material’s refractive index from a measured speed — for that, use this site’s index of refraction calculator instead.
How to use this calculator
- Enter both materials’ refractive indices and the incidence angle.
A worked example
Light traveling from air (n=1) into glass (n=1.5) at a 30° angle: refraction angle = 19.4712° — bending toward the normal as it enters the denser medium.
Light traveling from glass (n=1.5) back into air (n=1) at 20°: refraction angle = 30.8659° — bending away from the normal leaving the denser medium.
What the variables mean
| Variable | Meaning |
|---|---|
| n1, n2 | Refractive indices of the first and second medium |
| Angle 1 | Incident angle, measured from the normal |
Edge cases worth knowing
Light bends toward the normal entering a denser medium, and away from it leaving one — the two examples above show both directions of this exact rule.
At a large enough angle going from denser to less dense medium, total internal reflection occurs — no refraction angle exists at all, which is why the third test case (60° from glass into air) has no result. This is the same physics behind fiber optic cables trapping light inside.
Frequently asked questions
Why does light bend when entering a denser material?
Light slows down in a denser (higher refractive index) material, and that change in speed causes the light ray to bend toward the normal (perpendicular) line.
What is total internal reflection?
When light tries to pass into a less dense material at too steep an angle, no refracted ray can satisfy the equation — the light reflects entirely back instead of refracting through.
What’s a real-world example of Snell’s law?
A straw appearing bent where it enters water, or the design of eyeglass lenses and camera optics, all rely on this same refraction principle.
