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Snell’s Law Calculator

Find the angle of refraction.

Result

19.47 °
—

How it is calculated

Snell's law describes how a light ray bends when it crosses from one transparent medium into another: n1 sin θ1 = n2 sin θ2. The tool solves for the refracted angle: θ2 = arcsin(n1 sin θ1 / n2). Here n1 and n2 are the refractive indices of the first and second medium (for example about 1.00 for air and 1.33 for water), and the angle θ1 is the incidence angle in degrees, measured from the normal, the line perpendicular to the surface. The result is also in degrees from the normal. If the sine would exceed 1, no refracted ray exists and the tool reports total internal reflection (TIR). The second index must not be zero.

Worked example

A ray passes from air (n1 = 1) into glass (n2 = 1.5) with an incidence angle of 30 degrees. First, sin 30° = 0.5. Then sin θ2 = 1 × 0.5 / 1.5 = 0.3333. Taking the arcsine gives a refraction angle of 19.47 °. The ray bends toward the normal because it enters the denser medium, and the angle is smaller than 30 degrees. Going the other way, from glass to air, a 45 degree ray would give a sine above 1 and be totally reflected.

Try this example →

Common mistakes

  • Measuring the angle from the surface instead of from the normal; a ray at 30 degrees to the surface has an incidence angle of 60 degrees.
  • Swapping n1 and n2, which sends the ray the wrong way (toward the normal instead of away).
  • Entering the angle in radians when the tool expects degrees.
  • Expecting a number when the answer is TIR; this happens only when going from a denser to a less dense medium above the critical angle.
  • Using one refractive index for all colours; real materials bend blue light slightly more than red.

About this calculator

This calculator solves Snell's law, n₁ sin θ₁ = n₂ sin θ₂, to find the angle a light ray bends when it crosses the boundary between two materials with different refractive indices. Enter the incident angle and the two indices of refraction to get the refraction angle.

Optics students use it to work through textbook problems on lenses and prisms, while engineers use the same relationship to design camera lenses, eyeglasses, optical fibers, and anti-reflective coatings. It also flags total internal reflection when no real refraction angle exists.

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