Snell's Law Calculator

Calculate any variable in the Snell's Law equation: n₁sin(θ₁) = n₂sin(θ₂). Select the variable you want to find and enter the other values.

Examples

Explore common scenarios to understand how Snell's Law works.

Light from Air to Water

Angle of Refraction

Calculate the angle of refraction when light passes from air into water at an angle.

n₁: 1

θ₁: 30°

n₂: 1.33

Finding Incidence Angle

Angle of Incidence

Calculate the required angle of incidence in glass to get a specific refraction angle in water.

n₁: 1.52

n₂: 1.33

θ₂: 45°

Identify an Unknown Material

Refractive Index 2

Light enters an unknown material from water (1.33) at 45° and refracts at 32°. Find the material's refractive index.

n₁: 1.33

θ₁: 45°

θ₂: 32°

Total Internal Reflection

Total Internal Reflection

Show what happens when light goes from a dense to a less dense medium (glass to air) at a large angle.

n₁: 1.52

θ₁: 45°

n₂: 1

Other Titles
Understanding Snell's Law: A Comprehensive Guide
An in-depth look at the principles of refraction, the Snell's Law formula, and its applications in science and technology.

What is Snell's Law?

  • The Fundamental Principle of Refraction
  • Defining the Key Variables: n and θ
  • The Mathematical Formula: n₁sin(θ₁) = n₂sin(θ₂)
Snell's Law is a fundamental principle in optics that describes how light bends, or refracts, as it passes from one medium to another. This phenomenon occurs because the speed of light changes depending on the medium it is traveling through. The 'refractive index' (n) of a medium is a measure of how much it slows down light. A higher refractive index means a slower speed of light in that medium.
The Formula and Its Components
The law is expressed by the formula: n₁sin(θ₁) = n₂sin(θ₂). Here, n₁ is the refractive index of the first medium, θ₁ is the angle of incidence, n₂ is the refractive index of the second medium, and θ₂ is the angle of refraction. The angles are measured relative to the 'normal'—an imaginary line drawn perpendicular to the surface boundary between the two media.

Step-by-Step Guide to Using the Snell's Law Calculator

  • Choosing the Variable to Calculate
  • Entering Input Values Correctly
  • Interpreting the Results
Our calculator simplifies Snell's Law by allowing you to solve for any of the four variables in the equation.
How to Use

Total Internal Reflection and the Critical Angle

  • When Light Doesn't Refract
  • Calculating the Critical Angle
  • Conditions for Total Internal Reflection
A fascinating phenomenon called Total Internal Reflection (TIR) occurs when light travels from a denser medium (higher n) to a less dense medium (lower n). If the angle of incidence (θ₁) is greater than a specific 'critical angle', the light does not pass through to the second medium at all. Instead, it is completely reflected back into the first medium.
Critical Angle Formula
The critical angle (θcrit) can be calculated using the formula: θcrit = arcsin(n₂ / n₁), where n₁ > n₂. Our calculator will automatically detect when TIR occurs and display the critical angle.

Real-World Applications of Snell's Law

  • Fiber Optic Communication
  • Gemology and Diamond Brilliance
  • Optical Lenses and Vision Correction
Snell's Law isn't just a textbook formula; it's the principle behind many technologies and natural phenomena.
Key Applications

Common Misconceptions and Correct Methods

  • Angle Measurement: Always from the Normal
  • Refractive Index of a Vacuum vs. Air
  • Understanding Dimensionless Units
It's easy to make small mistakes when applying Snell's Law. A common error is measuring the angle from the surface instead of the normal. Remember, the angles θ₁ and θ₂ are always relative to the line perpendicular to the boundary.
Refractive Index Values
The refractive index of a vacuum is exactly 1. Air has a refractive index of approximately 1.00029, which is so close to 1 that for most calculations, using n=1.00 for air is sufficient. Remember that n is always greater than or equal to 1.