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Angle of Refraction Calculator

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Angle of refraction calculator helps you find the angle at which a beam of light or waves refracts as they pass from one medium to another, like from air to water. This can be useful for various applications such as in prisms, designing optical devices, and understanding how light behaves with different materials.

This is How Our Angle of Refraction Calculator Works:

We have made this angle of refraction calculator quite simple and user-friendly so that anyone can benefit from it by entering some inputs, such as:

What to Enter?

  • Select the parameters: First, select the parameters you want to calculate
  • Insert the values: Next, enter the values into their field accordingly

What will you Get?

Angle of Refraction: The exact angle of refraction in degrees along with step-by-step calculations
What is the Angle of Refraction?

“Angle of refraction is the bending of light as it travels from one medium to another. It is caused by the difference in the speed of light between the two mediums”.

It is normally denoted by $ θ_2 $.


When you look at a pencil in a glass of water, the pencil will appear to be bent a little bit at the waterline. This bending illusion happens because of refraction. Refraction occurs when light from the pencil changes direction as it moves from the water into the air. So, it's the reason why the pencil looks bent.

Angle of Refraction Formula?

The angle of refraction formula is a key part of finding the angle of refraction. Here is the formula that our angle of refraction calculator uses while functioning: 

$$ \sin(\theta_{2})=\frac{n_{1}\sin(\theta_{1})}{n_{2}} $$


  • $ n_1 $ is the refractive index of the first medium
  • $ n_2 $ is the refractive index of the second medium
  • $ θ_1 $ is the angle of incidence (the angle at which the light ray hits the surface)
  • $ θ_2 $ is the angle of refraction

How to Find Angle of Refraction?

The simplest way to find the angle of refraction is by using our free angle of refraction calculator. However, if you prefer manual calculations, you can follow the example provided below.


Suppose you have a ray of light passing from the air $ (n_1 = 1.00) $ into water $ (n_2 = 1.33) $.

The angle at which the light enters the water (angle of incidence) is 30 degrees $ (\theta_1 = 30^\circ) $.

Now, you want to find the angle at which the light is refracted inside the water (angle of refraction,$ \theta_2 $. 

Using the formula:

$ \sin(\theta_2) = \frac{n_1 \sin(\theta_1)}{n_2} $

Now put in the values:

$ \sin(\theta_2) = \frac{1.00 \cdot \sin(30^\circ)}{1.33} $

Calculate the value on the right side of the equation:

$ \sin(\theta_2) \approx 0.7075 $

Now, to find \theta_2, take the inverse sine (arcsine) of this value:

$ \theta_2 \approx \sin^{-1}(0.7075) \approx 45.0^\circ $

So, the angle of refraction inside the water is approximately 45.0 degrees.

Angle of Refraction for Various Mediums:

Let’s have a look at the following chart to understand how angle of refraction behaves through different mediums, such as:

Medium Refractive index Angle of refraction
Air 1.0003
Water 1.33 47.99°
Glass 1.52 61.5°
Diamond 2.42 73.5°
Acrylic 1.49 60.0°
Polystyrene 1.46 57.2°
Polyethylene 1.43 56.0°
PVC 1.54 62.5°


Why does Refraction Only Occur at an Angle?

Refraction only occurs at an angle because light travels at different speeds in different materials. When light travels from one medium to another, it slows down or speeds up depending on the refractive index of the second medium. The refractive index of a material is a measure of how much it slows down light.

How do you Increase the Angle of Refraction?

There are two ways to increase the angle of refraction:

  • Increase the angle of incidence: The angle of refraction is directly proportional to the angle of incidence. This means that the larger the angle of incidence, the larger the angle of refraction.
  • Increase the refractive index of the second medium: The angle of refraction is also directly proportional to the refractive index of the second medium. This means that the higher the refractive index of the second medium, the larger the angle of refraction.

How does Temperature Affect the Angle of Refraction?

As the temperature rises, the liquid becomes less dense and less viscous, allowing light to travel faster. Because of this, a smaller ratio leads to a smaller refractive index value. This means that the angle of refraction will also decrease when a material is heated.

What is the Angle of Refraction of Sunlight in the Atmosphere?

The angle of refraction of sunlight in the atmosphere is approximately 0.5 degrees. This causes the sun to appear slightly higher in the sky than it actually is.

What is Snell’s Law?

Snell's law is a law of physics that describes how light bends when it travels from one medium to another. It states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.

Snell's law can be expressed mathematically as follows:

$ n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2) $

References: Snell's law, Angle of Refraction

Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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