Case 1
- Refractive index of the first medium n₁
- 1
- Refractive index of the second medium n₂
- 1.33
- Angle of incidence θ₁
- 30°
22.0824°
Open with these valuesSnell's Law Calculator
22.0824°
Result: 22.0824 °Snell's law says n₁ × sin θ₁ = n₂ × sin θ₂, so the refraction angle is arcsin(n₁ × sin θ₁ ÷ n₂). Both angles are measured from the normal, in degrees. Past the critical angle no refracted ray exists and the calculator reads 90°, the grazing limit where total internal reflection sets in.
Worked examples
Case 2
- Refractive index of the first medium n₁
- 1.33
- Refractive index of the second medium n₂
- 1
- Angle of incidence θ₁
- 30°
41.6823°
Open with these valuesCase 3
- Refractive index of the first medium n₁
- 1.33
- Refractive index of the second medium n₂
- 1.52
- Angle of incidence θ₁
- 60°
49.2682°
Open with these valuesHow it's calculated
θ₂ = arcsin(n₁ × sin θ₁ ÷ n₂)
- StepEnter the index of the medium the light starts in — air 1.00, water 1.33, glass about 1.50.
- StepEnter the index of the medium it enters.
- StepEnter the angle of incidence, measured from the normal, not from the surface.
- ResultRead the refraction angle; 90° marks total internal reflection.
Reference table
| n₁, n₂, angle of incidence | Transition | Angle of refraction |
|---|---|---|
| 1, 1.33, 30 | Air into water, bends toward the normal | 22.0824 |
| 1, 1.5, 45 | Air into glass | 28.1255 |
| 1.33, 1, 30 | Water into air, bends away from the normal | 41.6823 |
| 1, 1, 40 | No change of medium, no bending | 40 |
| 1.33, 1.52, 60 | Water into glass | 49.2682 |
| 1.52, 1, 60 | Glass into air, past the critical angle | 90 |
Questions
How do I calculate the angle of refraction?
Take the sine of the angle of incidence, multiply by the first index, divide by the second, then take the inverse sine. Light going from air with n₁ = 1 into water with n₂ = 1.33 at 30° gives 22.0824°.
Why are the angles measured from the normal?
The normal is the imaginary line perpendicular to the surface, and Snell's law is written against it. That keeps the relationship consistent and makes a ray arriving head on, at 0° from the normal, pass through without bending.
Which way does light bend?
Into a denser medium with a higher index it bends toward the normal, so the refraction angle is smaller than the incidence angle. Into a less dense medium it bends away from the normal and the angle grows.
What does a result of 90° mean?
It marks total internal reflection. When light leaves a denser medium at a steep angle, the ratio n₁ × sin θ₁ ÷ n₂ passes 1 and no refracted ray exists any more — all the light reflects back, which is what keeps a signal inside an optical fibre. This calculator reports 90°, the grazing limit, rather than nothing at all.
What is a refractive index?
It says how much a medium slows light compared with a vacuum, which is exactly 1. Air is about 1.00, water 1.33, ordinary glass roughly 1.50 and diamond 2.42.
Sources and last check
Information, not professional advice.