Snell's Law Calculator

Calculate the refracted angle, critical angle, angular deviation, and total internal reflection status based on refractive indices and incident angle. Snell's Law Calculator helps students, educators, engineers, and optical professionals analyze light refraction between transparent media.

Highlights

  • Calculate refracted angles using Snell’s Law.
  • Determine the critical angle for total internal reflection.
  • Check whether total internal reflection occurs.
  • Find angular deviation between incident and refracted rays.
  • Calculate reflection angles in degrees or radians.

Table of Contents

  1. How Snell's Law Calculator Works?
  2. Practical Use Cases
  3. Accuracy and Limitations
  4. Quick Examples
  5. Frequently Asked Questions (FAQs)
  6. Cite This Calculator

How Snell's Law Calculator Works?

Snell's Law describes how a light ray changes direction when it passes between two transparent media with different refractive indices. The calculator uses n1 for the first medium, n2 for the second medium, and measures the incident and refracted angles from the normal to the interface.

n₁sin(θi)=n₂sin(θr)

The refracted angle is calculated by rearranging Snell's Law:

θr=sin−1(n1n2sin(θi))

If the second medium has a higher refractive index, the ray bends toward the normal. If it has a lower refractive index, the ray bends away from the normal.

When light travels from a higher-index medium to a lower-index medium, the calculator also determines the critical angle. This is the incident angle at which the refracted ray would lie along the boundary:

θc=sin−1(n2n1)

Total internal reflection occurs when n1 is greater than n2 and the incident angle is greater than the critical angle. Equivalently, the argument of the inverse-sine calculation for the refracted angle would be greater than 1, meaning no propagating refracted ray exists.

The remaining outputs are calculated as follows:


OutputCalculation or condition
Angular Deviation|θi−θr|
Reflection Angleθreflection=θi, according to the law of reflection
Total Internal ReflectionTrue when n1 > n2 and θi > θc

The calculator accepts refractive indices from 1 to 10 and an incident angle from 0 to 90 degrees or the equivalent supported angular representation.

Practical Use Cases

Physics students can enter the refractive indices of materials such as air, glass, or water and compare the predicted incident, refracted, and reflected angles while learning how light bends at an interface.

Teachers and educators can use the calculator to create demonstrations of Snell's Law, show how changing either refractive index affects the refracted angle, and illustrate the onset of total internal reflection.

Optical engineers can estimate ray behavior at boundaries in lenses, prisms, windows, and other optical components, including the angular deviation introduced by a change in medium.

Fiber-optics designers can check whether light traveling from a higher-index core toward a lower-index cladding reaches the critical angle and is likely to undergo total internal reflection.

Laboratory and imaging professionals can use the refracted-angle and reflection-angle results as quick theoretical references when aligning optical setups or interpreting rays crossing a flat material boundary.

Accuracy and Limitations

The calculator applies the ideal, geometric-optics form of Snell's Law to a flat boundary between homogeneous, isotropic, transparent media, using the supplied refractive indices and incident angle. It assumes angles are measured from the normal and does not model surface curvature, material absorption, scattering, polarization-dependent Fresnel reflectance, wavelength-dependent refractive index, or multiple interfaces. The critical-angle and total-internal-reflection results are meaningful only when the first refractive index is greater than the second; near the critical angle, small changes in the input values can noticeably change the result, and numerical rounding may affect the displayed final digits.

Quick Examples

Example #1: Air to Glass Refraction

Calculate how a 30-degree light ray bends when traveling from air into glass.

Example #2: Glass to Air Total Internal Reflection

Determine whether a light ray traveling from glass into air undergoes total internal reflection.

Example #3: Water to Air Critical-Angle Analysis

Analyze refraction and critical-angle behavior for light leaving water at an incident angle given in radians.

Frequently Asked Questions

Snell's law describes how light changes direction when it passes between materials with different refractive indices. It relates the refractive indices of the two media to the incident and refracted angles.

Incident, refracted, and reflected angles are measured from the normal, an imaginary line perpendicular to the interface. They are not measured from the surface itself.

Total internal reflection occurs when light travels from a higher-index medium to a lower-index medium and the incident angle exceeds the critical angle.

The light generally bends toward the normal because its speed decreases in the higher-index material. The exact change in direction depends on the two refractive indices and the incident angle.

Yes. The law of reflection states that the reflected ray makes the same angle with the normal as the incoming ray, regardless of the refracted ray's direction.

Cite This Calculator