Snell's Law Calculator

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Snell's Law Calculator - light refraction, angles and coefficients

Calculate how the direction of a light wave changes when passing between different media. The Snell's Law Calculator automatically determines the angle of refraction, refractive indicesn₁ i n₂and Fresnel reflection. An excellent tool for learning physics, optics and light engineering.

Snell's law refraction of light angle of incidence angle of refraction index of refraction optics Fresnel light wave

Launch the Snell Calculator View Formulas

What is Snell's Law

Snell's Law (also known as the law of refraction) describes the relationship between the angle of incidence and the angle of refraction when a light ray passes from one medium to another. Its classical form is:

n₁ · sin(θ₁) = n₂ · sin(θ₂)

where:

n₁– refractive index of the first medium,
n₂– refractive index of the second medium,
θ₁– angle of incidence,
θ₂– angle of refraction.

How the calculator works

You select known data: n₁, n₂, angle of incidence or refraction.
The calculator automatically solves the equation and provides missing values.
Additionally, it calculates the Fresnel reflection coefficients for s and p polarizations.
You can analyze the cases of total internal reflection and the critical angle of refraction.

Formulas used in calculations

Snell's Law:
n₁ sin(θ₁) = n₂ sin(θ₂)

Critical angle:
θ_c = arcsin(n₂ / n₁) (for n₁ > n₂)

Fresnel reflectance coefficients:
Rs = |(n₁ cosθ₁ - n₂ cosθ₂) / (n₁ cosθ₁ + n₂ cosθ₂)|²
Rp = |(n₁ cosθ₂ - n₂ cosθ₁) / (n₁ cosθ₂ + n₂ cosθ₁)|²

Average reflectance:
Ravg = (Rs + Rp) / 2

Practical examples

Air → Water

n₁ = 1.0003, n₂ = 1.333, θ₁ = 30°.

θ₂ = 22.03°, reflection Ravg ≈ 2.1%.

A typical case observed when looking from the air into the water.

Water → Air

n₁ = 1.333, n₂ = 1.0003, θ₁ = 60°.

Critical angle ≈ 48.75° → total internal reflection.

The ray does not leave the water - an effect used in optical fibers.

Glass → Air

n₁ = 1.5, n₂ = 1.0, θ₁ = 45°.

θ₂ = 71.8°, reflection Ravg ≈ 4.3%.

Example with optical lenses and prisms.

Air → Diamond

n₁ = 1.0, n₂ = 2.417, θ₁ = 35°.

θ₂ = 13.97°, reflection Ravg ≈ 16.8%.

Explains the unique brilliance of a diamond - its high refractive index.

Interpretation of results

If θ₂ < θ₁ – the wave bends towards the normal (entering a denser medium).
If θ₂ > θ₁ – the wave deviates from the normal one (entering a rarer medium).
With n₁ > n₂ and θ₁ > θ_c, complete reflection occurs.

Frequently asked questions (FAQ)

How to calculate the angle of refraction?

Use the formula: sin(θ₂) = (n₁ / n₂) · sin(θ₁). The calculator converts automatically for selected units.

Does the calculator take into account total internal reflection?

Yes. After exce