Snell's Law Calculator

Category: Physics
- March 20, 2025
| |

Snell's Law describes how light refracts when passing between different media, such as air to water or glass to air. The law states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of phase velocities in the two media, or equivalently, to the inverse ratio of the indices of refraction.

This calculator allows you to determine the angle of refraction, critical angle, and other optical properties using Snell's Law.

What would you like to calculate?

? The refractive index of the first medium (where light comes from). For air at standard conditions, use approximately 1.000.
? The refractive index of the second medium (where light enters). For water, use approximately 1.333.
degrees
? The angle between the incident ray and the normal to the interface (0-90 degrees).

Display Options

? Shows how refractive indices and angles vary with wavelength (dispersion effect). Note that this is an approximate model.

About Snell's Law

Snell's Law (also known as the law of refraction) describes the relationship between the angles of incidence and refraction when light passes through the boundary between two different isotropic media, such as air, glass, or water.

The Mathematical Expression:

Snell's Law is mathematically expressed as:

n₁ sin(θ₁) = n₂ sin(θ₂)

Where:

  • n₁ is the refractive index of the first medium
  • n₂ is the refractive index of the second medium
  • θ₁ is the angle of incidence (measured from the normal)
  • θ₂ is the angle of refraction (measured from the normal)
Critical Angle and Total Internal Reflection:

When light passes from a medium with a higher refractive index to one with a lower index (n₁ > n₂), there exists a critical angle of incidence (θc) at which the refracted light travels along the boundary between the two media.

For angles of incidence greater than the critical angle, all light is reflected back into the first medium - a phenomenon called total internal reflection.

The critical angle is given by:

θc = arcsin(n₂/n₁)
Refractive Indices of Common Materials:
Material Refractive Index (approximate)
Vacuum 1.0000 (exact)
Air (at STP) 1.0003
Water 1.333
Ethanol 1.36
Crown Glass 1.52
Flint Glass 1.62
Diamond 2.42

Note: Refractive indices vary with the wavelength of light.

Key Applications:
  • Optical Systems: Lenses, prisms, fiber optics, and other optical components in cameras, microscopes, and telescopes.
  • Gemology: The brilliance of diamonds and other gemstones is due to their high refractive indices.
  • Fiber Optic Communications: Total internal reflection keeps light signals inside optical fibers.
  • Medical Imaging: Endoscopes and other medical optical instruments use principles of refraction.
  • Atmospheric Optics: Mirages, rainbows, and the twinkling of stars are all related to refraction.

What is the Snell's Law Calculator?

The Snell's Law Calculator is a tool that helps you determine how light bends when it moves between different materials. It uses Snell’s Law, a fundamental principle in physics, to calculate the angle at which light refracts or reflects.

Light changes direction when it travels from one medium to another, such as from air to water or from glass to air. This bending occurs because different materials have different refractive indices, which affect the speed of light.

With this calculator, you can compute:

  • The angle of refraction when light enters a new medium.
  • The angle of incidence needed to produce a specific refraction.
  • The critical angle at which total internal reflection occurs.
  • The refractive index of a material based on light behavior.

Formula Used in the Calculator

Snell's Law is mathematically expressed as:

n₁ × sin(θ₁) = n₂ × sin(θ₂)

Where:

  • n₁ – Refractive index of the first medium.
  • n₂ – Refractive index of the second medium.
  • θ₁ – Angle of incidence (angle at which light enters the medium).
  • θ₂ – Angle of refraction (angle at which light bends in the new medium).

For cases where total internal reflection occurs, the critical angle (θc) is calculated as:

θc = arcsin(n₂ / n₁)

Here, total internal reflection happens when light moves from a denser medium to a less dense medium (where n₁ > n₂).

How to Use the Calculator

Follow these steps to use the Snell's Law Calculator effectively:

  1. Select what you want to calculate. Choose from angle of refraction, angle of incidence, critical angle, or refractive index.
  2. Enter the refractive indices. Input the refractive index of the first and second medium. You can also select common material pairs from a dropdown list.
  3. Provide the required angle. Depending on your calculation type, enter either the angle of incidence or the angle of refraction.
  4. Click "Calculate". The tool will instantly compute the result based on Snell’s Law.
  5. Review the results. The calculator will display the calculated values, including angles and refractive indices. If total internal reflection occurs, the result will indicate it.

Why is Snell’s Law Useful?

Snell's Law is essential in various fields, including:

  • Optics and Lenses: Helps design eyeglasses, microscopes, and cameras.
  • Fiber Optic Communications: Used in transmitting data efficiently through optical fibers.
  • Medical Imaging: Essential for technologies like endoscopes that use light refraction.
  • Gemology: Explains why diamonds sparkle due to their high refractive index.
  • Astronomy: Helps understand atmospheric refraction and optical illusions like mirages.

Frequently Asked Questions (FAQ)

1. What is the refractive index?

The refractive index (n) of a material is a measure of how much light slows down when traveling through it. Air has a refractive index of about 1.0003, water is around 1.333, and glass varies between 1.5 and 1.6.

2. What happens if the angle of incidence is greater than the critical angle?

If the angle of incidence exceeds the critical angle, light does not refract into the second medium. Instead, it undergoes total internal reflection and remains within the first medium.

3. Can the calculator handle different light wavelengths?

Yes, the tool allows you to include wavelength-dependent effects. Refractive indices change slightly based on the color of light, which affects refraction angles.

4. Why does light bend when entering a new medium?

Light bends because its speed changes when moving between materials with different optical densities. A higher refractive index means light slows down more, causing it to bend toward the normal.

5. What are some real-world examples of refraction?

Refraction is seen in:

  • A straw appearing bent in a glass of water.
  • The way lenses in eyeglasses and cameras focus light.
  • Rainbows forming due to light bending through raindrops.
  • The shimmering effect on hot roads caused by atmospheric refraction.

Conclusion

The Snell’s Law Calculator is a simple and powerful tool for understanding how light bends as it moves through different materials. Whether you’re studying physics, working with optical systems, or just curious about how lenses and prisms work, this tool provides quick and accurate calculations based on Snell’s Law.