Snell's Law Calculator
Calculate snell's law instantly in your browser — the published formula, worked locally with no data sent anywhere.
Loading calculator…
What this tool does
Calculate snell's law instantly in your browser — the published formula, worked locally with no data sent anywhere. Refractive indices are for visible light near the sodium D line (water 1.333, crown glass ≈ 1.52, diamond 2.42). Dispersion means the index — and the bending — differs slightly by colour, which is how prisms split rainbows.
How to use the Snell's Law Calculator
- Enter or select refractive index of first medium (n₁).
- Enter or select angle of incidence (degrees, from the normal).
- Enter or select refractive index of second medium (n₂).
- Read the calculated result; change any measurement to compare alternatives.
Formula
Snell's law: n₁·sin θ₁ = n₂·sin θ₂. Angles are measured from the normal (the line perpendicular to the surface). If sin θ₂ would exceed 1, total internal reflection occurs instead.
- n1
- Refractive index of first medium (n₁)
- theta1
- Angle of incidence (degrees, from the normal)
- n2
- Refractive index of second medium (n₂)
Refractive indices are for visible light near the sodium D line (water 1.333, crown glass ≈ 1.52, diamond 2.42). Dispersion means the index — and the bending — differs slightly by colour, which is how prisms split rainbows.
Worked example
For snell's law calculator, the following measurements illustrate the exact method: Refractive index of first medium (n₁): 1; Angle of incidence (degrees, from the normal): 45; Refractive index of second medium (n₂): 1.333.
Inputs
- Refractive index of first medium (n₁)1
- Angle of incidence (degrees, from the normal)45
- Refractive index of second medium (n₂)1.333
Result
- Angle of refraction (degrees)32.04
- Direction of bendingToward the normal (slows down entering the denser medium)
Results explained
- Angle of refraction (degrees)
- Angle of refraction (degrees) from the formula above. Refractive indices are for visible light near the sodium D line (water 1.333, crown glass ≈ 1.52, diamond 2.42). Dispersion means the index — and the bending — differs slightly by colour, which is how prisms split rainbows.
- Direction of bending
- Direction of bending from the formula above. Refractive indices are for visible light near the sodium D line (water 1.333, crown glass ≈ 1.52, diamond 2.42). Dispersion means the index — and the bending — differs slightly by colour, which is how prisms split rainbows.
Frequently asked questions
Snell's law: n₁·sin θ₁ = n₂·sin θ₂. Angles are measured from the normal (the line perpendicular to the surface). If sin θ₂ would exceed 1, total internal reflection occurs instead.
Refractive indices are for visible light near the sodium D line (water 1.333, crown glass ≈ 1.52, diamond 2.42). Dispersion means the index — and the bending — differs slightly by colour, which is how prisms split rainbows.
Every field is labelled with its unit — enter values in exactly the labelled unit and read the result in the labelled output unit. Fields with a unit symbol also support the site-wide imperial/metric switch, which converts before the formula runs.
It uses double-precision arithmetic and the published constants and formulas named on this page. The last displayed digit may be rounded, and real conditions can differ from the idealized model described in the assumptions.
Yes. Every calculation runs entirely in your browser; nothing you enter is uploaded, stored or shared.