Snell's Law Calculator

Calculate refracted angle from refractive indices and an incident angle.

Check Snell's Law Calculator

Refracted angle
25.5476 deg
Computed from n1 * sin(theta1) = n2 * sin(theta2).
Critical angle
Not applicable
Shown only when light moves from a denser to a less dense medium.

Formula result

Check before you use it

What the numbers show

Refracted angle output

The result shows how much the ray bends when it moves between media with different refractive indices.

Critical angle support

Use snell's law calculator for refraction problems, critical-angle checks, and basic optics setup.

Handles total internal reflection

A higher refractive index usually bends the ray closer to the normal.

Copy-ready formula handoff

Use this after solving the live calculator result, then paste the answer into a lab note, homework check, or engineering review.

Formula

n1 * sin(theta1) = n2 * sin(theta2)

Inputs to check
  • Incident medium index: Refractive index of the starting medium.
  • Incident angle: Angle measured from the normal in the first medium.
  • Refracted medium index: Refractive index of the second medium.
  • Refracted angle: Angle measured from the normal in the second medium.
Before copying
  • Angles are measured from the surface normal, not from the surface itself.
  • The interface is treated as clean and ideal.
  • Measuring the incident angle from the surface instead of from the normal line.
  • Ignoring total internal reflection when the solved sine value would be greater than 1.
Snell's Law Calculator result: [paste the solved value from the calculator above].
Formula used: n1 * sin(theta1) = n2 * sin(theta2)
Inputs checked: Incident medium index, Incident angle, Refracted medium index, Refracted angle.
Assumptions: Angles are measured from the surface normal, not from the surface itself. The interface is treated as clean and ideal.
Worked example: Light moves from air (1.00) into glass (1.50) at 30 degrees. Enter n1 = 1.00, theta1 = 30 deg, and n2 = 1.50. Solve n1*sin(theta1) = n2*sin(theta2). Result: theta2 is smaller than theta1 because the ray bends toward the normal.
Next check: Measuring the incident angle from the surface instead of from the normal line.

Equation context

Built for refraction problems, critical-angle checks, and basic optics setup. This page pairs the live calculator with the governing formula, variable glossary, and a worked example so the result is easier to trust and reuse.

Quick entry points

Use the calculator to verify arithmetic after you set up the formula yourself.

Change one input at a time to see which variable is driving the result.

Review the formula notes before using the answer in a lab or design check.

Variables to track

n1
Incident medium index

Refractive index of the starting medium. Unit: -.

theta1
Incident angle

Angle measured from the normal in the first medium. Unit: deg.

n2
Refracted medium index

Refractive index of the second medium. Unit: -.

theta2
Refracted angle

Angle measured from the normal in the second medium. Unit: deg.

Formula method and unit assumptions

Formula and example

n1 * sin(theta1) = n2 * sin(theta2)

Worked example

Light moves from air (1.00) into glass (1.50) at 30 degrees

  1. 1Enter n1 = 1.00, theta1 = 30 deg, and n2 = 1.50.
  2. 2Solve n1*sin(theta1) = n2*sin(theta2).
  3. 3Result: theta2 is smaller than theta1 because the ray bends toward the normal.

Snell law gives the geometry of the ray path, which is often the first step before handling lenses or critical-angle reasoning.

incident rayrefracted raynormal

Assumptions

Angles are measured from the surface normal, not from the surface itself.
The interface is treated as clean and ideal.
The calculator does not model reflection intensity or dispersion effects.

Common mistakes

Measuring the incident angle from the surface instead of from the normal line.
Ignoring total internal reflection when the solved sine value would be greater than 1.
Using refractive indices for the wrong wavelength when dispersion matters.

Equation context and next checks

Formula and variable setup for Snell's Law Calculator

Calculate refracted angle from refractive indices and an incident angle. The page is designed to help you move from the known values to the correct formula without rebuilding the derivation every time.

For snell's law calculator, the safest workflow is to confirm the unit system first, then map each symbol to the physical quantity in your problem statement before solving.

  • n1: Incident medium index (-) - Refractive index of the starting medium.
  • theta1: Incident angle (deg) - Angle measured from the normal in the first medium.
  • n2: Refracted medium index (-) - Refractive index of the second medium.
  • theta2: Refracted angle (deg) - Angle measured from the normal in the second medium.

How to read the result

The result shows how much the ray bends when it moves between media with different refractive indices.

This tool is especially useful for refraction problems, critical-angle checks, and basic optics setup. The output becomes more trustworthy when you compare nearby cases instead of relying on one single run.

  • Refracted angle output
  • Critical angle support
  • Handles total internal reflection

Assumptions and limits

The calculator applies the standard textbook relation for this topic, which makes it a strong first-pass answer but not always a full real-world model.

Before you use the result in a lab, design review, or report, check whether the simplified assumptions still match the physical system you care about.

  • Angles are measured from the surface normal, not from the surface itself.
  • The interface is treated as clean and ideal.
  • The calculator does not model reflection intensity or dispersion effects.

Quick glossary

Incident medium index

Refractive index of the starting medium.

Incident angle

Angle measured from the normal in the first medium.

Refracted medium index

Refractive index of the second medium.

Ideal model

A simplified physics model that omits secondary effects so the first-order relationship is easier to inspect.

Formula checks before using the result

Formula questions

Checks before using the result

When should I use the snell's law calculator?

Use snell's law calculator for refraction problems, critical-angle checks, and basic optics setup, especially when the governing formula is already known and the main need is a fast, transparent calculation.

What is the main thing the snell's law calculator tells me?

The result shows how much the ray bends when it moves between media with different refractive indices.

What can make the snell's law calculator answer inaccurate?

The answer is exact for the formula and assumptions on the page, but it can drift when the real system violates those assumptions. Common limits include Angles are measured from the surface normal, not from the surface itself. The interface is treated as clean and ideal. The calculator does not model reflection intensity or dispersion effects.

Formula references and related examples

Formula Basis

Formula Notes And References

A higher refractive index usually bends the ray closer to the normal.
If the sine relation demands a value above 1, the setup implies total internal reflection.