Snell's Law Calculator

Category: Physics
- October 30, 2025
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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, fibre 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.
  • Fibre Optic Communications: Total internal reflection keeps light signals inside optical fibres.
  • 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.

Understanding Snell's Law

Snell's Law explains how light bends when it moves from one material to another. Imagine light travelling from air into water or glass. The law states that the angle at which light enters a new medium is related to how fast light travels in that medium. This relationship helps us understand how lenses work in glasses and cameras.

What Is the Snell's Law Calculator?

The Snell's Law Calculator is a handy tool that helps you figure out different angles of refraction, incidence, and even the critical angle when light passes from one material to another. With just a few inputs, you can discover how light behaves in various situations, making it useful for students, teachers, and anyone curious about optics.

How to Use the Calculator

  • Input the refractive index values for the two media.
  • Enter the angle of incidence.
  • Select the type of calculation you want to perform—like finding the angle of refraction or the critical angle.

This simple process can lead to quick insights about light’s behaviour in different mediums.

What Can You Calculate?

The calculator offers several options for calculations. You can find:

  • Angle of Refraction: How much light bends when entering a new medium.
  • Angle of Incidence: The angle at which light hits the surface.
  • Critical Angle: The angle beyond which light cannot pass into the second medium and is instead reflected.
  • Refractive Index: A measure of how much light slows down in a medium.

These calculations are essential for various applications in Physics and optics.

Why Is This Important?

Understanding how light refracts is vital in many fields. It helps in designing optical devices, understanding natural phenomena like rainbows, and even in developing Technology like fibre optics. The insights gained from the Snell's Law Calculator can enhance learning in Science classes and practical applications in engineering and design.

Common Materials and Their Indices

When using the calculator, you can choose from common materials that have known refractive indices. Here are a few examples:

  • Air: Approx. 1.000
  • Water: Approx. 1.333
  • Glass: Ranges from 1.5 to 1.9 depending on the type
  • Diamond: Approx. 2.42

This helps in easily setting up calculations without needing to look up each material's properties.

Benefits of the Calculator

The Snell's Law Calculator is user-friendly and provides instant results, making it perfect for quick experiments or homework help. It can be used in a classroom setting to engage students with hands-on learning about light and optics. Its ability to handle different materials and angles allows users to explore various scenarios in an interactive way.

Exploring Further with Snell's Law

By using the Snell's Law Calculator, you can also delve deeper into related topics, such as total internal reflection and how different wavelengths of light interact with materials. This knowledge is not only academically enriching but also connects to real-world applications in technology, art, and nature.