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Snell's Law Calculator

Calculate how a light ray refracts at a boundary between two media from an incident angle and two user-supplied refractive indices.

How It Works

Formula

n1sin⁡(θ1)=n2sin⁡(θ2)n_1 \sin(\theta_1) = n_2 \sin(\theta_2)

θc=arcsin⁡(n2n1)\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)

Variables, symbols and units

n1n_1

Refractive index of medium 1(dimensionless)

n2n_2

Refractive index of medium 2(dimensionless)

θ1\theta_1

Incident angle from the normal(°)

θ2\theta_2

Refracted angle from the normal(°)

θc\theta_c

Critical angle for total internal reflection(°)
Calculation method explained

Enter the incident angle from the normal in degrees, then enter the dimensionless refractive indices n1 and n2 for the two media. The calculator stays focused on one boundary: it solves the transmitted angle when a real refracted ray exists and switches to a total-internal-reflection result when it does not.

The calculator applies Snell’s law n1sin⁡(θ1)=n2sin⁡(θ2)n_1 \sin(\theta_1) = n_2 \sin(\theta_2). All angles are measured from the normal. When n1>n2n_1 > n_2, it also computes the critical angle θc=arcsin⁡(n2/n1)\theta_c = \arcsin(n_2 / n_1). If θ1>θc\theta_1 > \theta_c, there is no real transmitted ray, so the result becomes total internal reflection instead of a fake angle. Refractive indices here are user-supplied dimensionless inputs, not built-in material references, and real values can vary with wavelength, temperature, and material conditions.

Frequently Asked Questions

What does “angle from the normal” mean?
The normal is an imaginary line perpendicular to the boundary. Measure θ1 and θ2 from that line, not from the surface itself.
When does total internal reflection happen?
It happens only when light travels from a higher refractive index into a lower one and the incident angle is larger than the critical angle. Then Snell’s law has no real transmitted-angle solution.
Why does a critical angle not always appear?
A critical angle applies only when n1 is greater than n2. If light is moving into an equal or higher index medium, there is no total-internal-reflection threshold for that direction.
Why are there no material presets or refractive-index tables?
This calculator is intentionally not a materials database. It uses the indices you provide, so it does not imply unsourced exact values for glass, acrylic, water, or any other medium.
How accurate is the result if refractive indices vary?
The math is exact for the values entered, but real refractive indices can shift with wavelength, temperature, and material conditions. The result is only as good as the indices you supply.

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