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Refraction · Optics

Snell’s Law Refraction Calculator

Find the refracted angle from two refractive indices and detect total internal reflection.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Angles measured from the normal to the boundary

Law of refraction

n₁ sin θ₁ = n₂ sin θ₂

Critical angle

θc = arcsin(n₂/n₁), n₁ > n₂
Optics calculator

Refraction at a boundary

An incident ray in Air, dry (1 atm) meets the boundary at 30 degrees from the normal. The refracted ray enters Crown glass (N-BK7) at 19.25254990295931 degrees from the normal.Upper: Air, dry (1 atm)n₁ = 1.000277Lower: Crown glass (N-BK7)n₂ = 1.5168normalboundary incident rayrefracted rayθ₁ = 30°θ₂ = 19.253°
Angles are measured from the normal.Air, dry (1 atm) → Crown glass (N-BK7)

Indices are approximate sodium-D values at 20 °C; dry air assumes 1 atm. The selected upper medium contains the incident ray.

n₁sinθ₁=n₂sinθ₂

Select both media and calculate the refracted angle or total-reflection condition.

Using the model

Symbols, assumptions and limitations

Interpretation notes

Angles are measured from the normal. Refractive indices depend on wavelength, temperature, and material conditions.

Worked examples

See the method in practice

01

Air to glass

At 30° from air into n = 1.5 glass, the refracted angle is about 19.47°.

02

Total internal reflection

From glass to air, sufficiently large incident angles do not produce a transmitted ray.

Questions

Frequently asked

Why measure from the normal?

Snell’s law is defined using the angle between each ray and the surface normal.

When is total internal reflection possible?

Only when light travels from a higher refractive index to a lower one above the critical angle.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — refraction

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology