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Angle of Refraction Calculator

This calculator will determine the angle of refraction or refractive index based on the inputs you provide.

Choose a Calculation

Refractive Index 1

Medium 1 (n₁)

Refractive Index 2

Medium 2 (n₂)

Angle of Incidence (θ₁)

deg ▾

Angle of Incidence (θ₁)

deg ▾

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Use our advanced angle of refraction calculator to determine the angle at which a light ray bends when entering a different medium. The calculator also provides detailed steps for finding the refractive index, which describes how much light bends in a material.

How to Find the Angle of Refraction?

The angle of refraction is the angle at which light bends when it passes from one medium into another. Refraction occurs because light travels at different speeds in different materials. The key quantities are the angle of incidence and the angle of refraction, related by Snell’s Law:

Angle of Refraction Formula:
θ₂ = sin⁻¹((n₁ × sin θ₁) / n₂)

Where:

n₁ = refractive index of the first medium
n₂ = refractive index of the second medium
θ₁ = angle of incidence
θ₂ = angle of refraction

Understanding Incidence and Refraction:

If light enters a medium with a higher refractive index from a lower one, the angle of refraction is smaller than the angle of incidence. Example: vacuum to air.
If light enters a medium with a lower refractive index from a higher one, the angle of refraction is larger than the angle of incidence. Example: air to water.

The refractive index of each medium is constant. Using an angle of refraction calculator, you can quickly find the bending angle for any combination of media and incidence angles.

Practical Example:

A ray of light passes from air into water. Air has a refractive index of 1.000293, and water has a refractive index of 1.333. The angle of incidence is 7°. Find the angle of refraction.

Given:

n₁ = 1.000293 (air)
n₂ = 1.333 (water)
θ₁ = 7°

Solution:

Using Snell’s Law: θ₂ = sin⁻¹((n₁ × sin θ₁) / n₂)

Substitute the values: θ₂ = sin⁻¹((1.000293 × sin 7°) / 1.333)

θ₂ ≈ 5.23°

Using the Angle of Refraction Calculator:

Our calculator simplifies the process. Enter the values below to get instant results and a step-by-step solution.

Input:

Select the calculation parameter
Choose the mediums involved
Enter the angle of incidence
Click Calculate

Output:

Calculated angle of refraction
Detailed solution steps

Angle of Refraction for Common Mediums:

The following table shows refractive indices for common materials:

Medium	Refractive Index (n)
Vacuum	1.000
Air	1.000293
Water (20°C)	1.333
Ethanol	1.36
Ice	1.31
Diamond	2.419

Knowing the refractive index allows you to understand how light bends when moving between media, and this calculator provides accurate results for any combination.

FAQs

Why is the Refractive Index Dimensionless?

It is a ratio of the speed of light in vacuum to the speed of light in the medium. Since it is a ratio of two speeds, it has no units.

References:

Sources: Wikipedia – Snell’s Law, explanation and calculation of angle of refraction

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