Snell's Law Calculator
Calculate refracted angle from refractive indices and an incident angle.
Check Snell's Law Calculator
Formula result
Check before you use it
What the numbers show
The result shows how much the ray bends when it moves between media with different refractive indices.
Use snell's law calculator for refraction problems, critical-angle checks, and basic optics setup.
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.
n1 * sin(theta1) = n2 * sin(theta2)
- 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.
- 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
Refractive index of the starting medium. Unit: -.
Angle measured from the normal in the first medium. Unit: deg.
Refractive index of the second medium. Unit: -.
Angle measured from the normal in the second medium. Unit: deg.
Formula method and unit assumptions
Formula and example
Worked example
Light moves from air (1.00) into glass (1.50) at 30 degrees
- 1Enter n1 = 1.00, theta1 = 30 deg, and n2 = 1.50.
- 2Solve n1*sin(theta1) = n2*sin(theta2).
- 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.
Assumptions
Common mistakes
Related formula checks
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
Refractive index of the starting medium.
Angle measured from the normal in the first medium.
Refractive index of the second medium.
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