Snell's Law Calculator

Select the parameter and enter the required values. The tool will calculate the result using Snell's law, with detailed steps provided

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Window Glass 1

Refractive Index 1 (n₁)

Angle of Incidence (θ₁)

deg ▾

Angle of Incidence (θ₂)

deg ▾

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Snell's Law Calculator

The Snell's Law calculator measures the refraction of light as it passes from one medium to another. It can determine the angle of refraction, angle of incidence, or the ratio of refractive indices between two media.

What is Snell's Law?

Snell's Law describes the relationship between the angle of incidence and the angle of refraction when light enters a different medium.

Light bends depending on the refractive index of the medium. When light moves from one medium to another (like air to water), its wavelength and speed change, causing it to bend towards or away from the normal. A Snell's Law calculator computes the refractive index based on these changes.

Snell's Law Equation

The basic formula is:

n₁ sin θ₁ = n₂ sin θ₂

Where:

n₁ = refractive index of medium 1
n₂ = refractive index of medium 2
θ₁ = angle of incidence
θ₂ = angle of refraction

Alternatively, the law can be written as:

sin i / sin r = μ

i = angle of incidence
r = angle of refraction
μ = ratio of refractive indices of the two media

Practical Example:

Calculate the angle of refraction for light moving from air into water:

Refractive index of air: n₁ = 1.000293
Refractive index of water: n₂ = 1.333
Angle of incidence: θ_i = 30° = 0.5236 rad

Using Snell's Law:

θ_r = sin^-1((n₁ * sin θ_i) / n₂)

Substitute the values:

θ_r = sin^-1((1.000293 * sin(0.5236)) / 1.333) ≈ 22.04°

The light bends towards the normal when entering water from air.

Refractive Indices of Common Media

Medium	Refractive Index
Air	1.000293
Carbon Dioxide	1.000449
Hydrogen	1.000132
Methane	1.000444
Nitrogen	1.000298
Oxygen	1.000271
Milk	1.35
Olive Oil	1.47
Water	1.333
Glass	1.5 – 1.62
Diamond	2.417
Polycarbonate	1.59