Snell's Law Calculator

Light entering water from air at 30° to the normal bends towards the normal to an angle of 22.0301 °, from Snell’s law n₁ sin θ₁ = n₂ sin θ₂.

Solve for:

Angle of refraction θ₂Refractive index 1 n₁Angle of incidence θ₁Refractive index 2 n₂

Refractive index 1 n₁:

Air 1.000 (1.0003), water 1.333, glass about 1.5, diamond 2.417.

Angle of incidence θ₁:

Refractive index 2 n₂:

Angle of refraction θ₂ =

22.030108725579 °

Precision

Full answer, then cut to fewer decimals (not rounded):

22.030108725579 °
22.03010872557 °
22.0301087255 °
22.030108725 °
22.03010872 °
22.0301087 °
22.030108 °
22.03010 °
22.0301 °
22.030 °
22.03 °
22.0 °

Critical angle: none (light enters the denser medium, n₂ ≥ n₁)
Speed in medium 2 (c/n₂): 224900.5686 km/s

Step-by-step solution

θ₂ = arcsin(n₁ × sin θ₁° ÷ n₂)
θ₂ = arcsin(1 × sin 30° ÷ 1.333)
θ₂ = 22.03010873 °

Snell's Law Formula

n₁ sin θ₁ = n₂ sin θ₂

n refractive index of each medium, θ angle measured from the normal; critical angle θc = arcsin(n₂/n₁)

Worked Example

Light passing from air (n = 1) into water (n = 1.333) at 30° to the normal:

θ₂ = arcsin(n₁ × sin θ₁° ÷ n₂)
θ₂ = arcsin(1 × sin 30° ÷ 1.333)
θ₂ = 22.03010873 °

Speed in medium 2 (c/n₂): 224900.5686 km/s

Common refractive indices

Vacuum 1 (exactly), air 1.0003, water 1.333, crown glass about 1.52, acrylic 1.49, diamond 2.417. Values vary slightly with wavelength, which is why prisms split white light.

More Waves and Optics Calculators

Wave Speed Calculator

v = f λ

v wave speed, f frequency (Hz), λ wavelength; period T = 1/f

Example: Concert A (440 Hz) travelling through air at 343 m/s: Wavelength λ = 0.779545 m.

Open the wave speed calculator →
Lens and Mirror Equation Calculator

1/f = 1/dₒ + 1/dᵢ, m = −dᵢ/dₒ

f focal length, dₒ object distance, dᵢ image distance (real-is-positive convention); m magnification

Example: An object 15 cm from a converging lens with f = 10 cm: Image distance dᵢ = 30 m.

Open the lens and mirror equation calculator →

Frequently asked questions

What is total internal reflection?

Going from a denser to a less dense medium (n₁ > n₂), beyond the critical angle no refracted ray exists and all light reflects. Optical fibres and diamonds rely on it.

Are angles measured from the surface or the normal?

From the normal, the line perpendicular to the surface. If you have the angle to the surface, subtract it from 90°.

Sources

The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .

Last reviewed: 2026-10-15. Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.

Cite this page

APA

Scientific Converters. (2026, October 15). Snell's Law Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/snells-law-calculator/

IEEE

Scientific Converters, "Snell's Law Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/snells-law-calculator/