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Or # Angle of Refraction Calculator

This calculator will calculate the angle of refraction or refractive index with respect to the inputs you provide.

Choose a Calculation

Medium 1

Refractive Index 1 (n₁)

Medium 2

Refractive Index 2 (n₂)

Angle of Incidence (θ₁)

Angle of Refraction (θ₂) Table of Content

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Use our advanced angle of refraction calculator that helps you to calculate at which angle a certain beam of light refracts. It also provides complete work for the refractive index, a particular property that refers to the bending of light.

## How to Find Angle of Refraction?

The angle of refraction represents the angle at which the light ray bends when entering one medium to another. The main reason for refraction is that light travels at various speeds via various mediums.

The angle of incidence and angle of refraction is the fundamental concepts.

The relationship is described by Snell’s laws, you can calculate the angle of refraction by the given formula:

Angle of refraction formula = (n₁ * sin(θ₁)) / sin(θ₂)

Where

• n1 & n2 =  the refractive index of the medium
• θ1 =  angle of incidence
• θ2 = angle of refraction

### The Angle of Incidence and Refraction:

The angle of incidence and angle of refraction can be predicted by the following consideration:

• If the light enters from a medium of lower refractive index to a higher refractive index. Then the angle of refraction will be smaller than the angle of incidence. For example, light enters from vacuum to air.
• On the other hand, If the light enters from a medium with a higher refractive index to a lower refractive index. Then the angle of refraction will be larger than the angle of incidence. For example, light enters from the air into water.

The refractive index of a medium is fixed and it can’t be changed. You can find what is the angle of refraction of a certain medium by the angle of refraction calculator. It’s important to note that the angle of refraction is dependent on the properties of the two media involved and the angle of incidence.

### Practical Example:

Suppose the light is entering from air to water, the refractive indexes of the air and water are 1.000293 and 1.333 respectively. If the angle of incidence is 7 degrees, then what is the angle of refraction?

#### Given:

n₁ is the refractive index of medium 1 = 1.000293

n₂ is the refractive index of medium 2 = 1.333

The angle of Incidence (θ₂) = 0.1221731

#### Solution

Formula = sin-1((n₂ * sin(θ₂)) / n₁)

Put values into a formula

θ₁ = sin-1((1.333 * sin(0.1221731)) / 1.000293);

θ₁ = 9.346483

## Working of Angle of Refraction Calculator:

It is not complicated to calculate the angle of refraction with the refraction angle calculator.

Let’s see how?

Input:

• First, select the parameter you want to calculate
• As per your selection, make a choice for the medium from the next list
• Now enter the angle of incidence and refraction
• Tap Calculate

Output:

• Angle of refraction
• Step-by-step calculation

### The Angle of Refraction of Various Mediums:

The angle of refraction of various mediums is given as under:

Medium Refractive index
Vacuum 1 (by definition)
Air 1.000293
Water at 20 °C 1.333
Ethanol 1.36
Ice 1.31
Diamond 2.419

The angle of incidence and refraction is different for various mediums, so it is essential to know which wave types refract when crossing from one medium to another.

## FAQs:

### Why is the Refractive Index Dimensionless?

The refractive index is a dimensionless value and a ratio between the angle of incidence and the angle of refraction.

## References:

From the source Wikipedia: Angle of Refraction, How to find Refraction?