Calculate Refraction

A simple calculator for the angle of incidence, angle of refraction and the refractive index and for the speed of light in a medium. Light is refracted, if a light beam goes from one transparent medium into another without being reflected. If the light beam doesn't hit the border perpendicularly, then at this border the angle changes. The refractive index for water is 1.33, for window glass it is 1.46. The refractive index also tells about the ratio of the speed of light in vacuum and in a medium.
Please enter two values per calculator, the third value will be calculated.

Angle of incidence α:		°
Angle of refraction β:		°
Refractive index n:

Decimal places:

Example: in the graphic above, the angle of incidence is about 38 degrees and the angle of refraction is about 35 degrees. This results in a refractive index of 1.07. Gases usually have lower values, liquids and solids mostly have higher values. This value can be achieved with aerogels, for example, or with artificial meta-materials. It can also be achieved with gas mixtures under high pressure.

Speed of light in vacuum, c₀:		km/s
Speed of light in medium, c₁:		km/s
Refractive index n:

Decimal places:

Example: conventional glass has a refractive index of approximately 1.5. This means that the speed of light in this medium is almost 200,000 kilometers per second, about 100,000 less than in a vacuum.

Formulas:
n = sin(α) / sin(β)
n = c₀ / c₁

What follows is complicated and confusing, but that's just how nature is sometimes. There are a few very special materials with a refractive index of less than one. In these materials, the speed of light is higher than in a vacuum. As an extreme example, gaseous caesium has a refractive index of 0.35 for certain wavelengths in the absorption resonance range, around 894 and 852 nanometers. The speed of light of that wavelength in this medium would therefore be 856,550 kilometers per second. This is a phase velocity effect, whereby neither information nor energy is transferred, and therefore does not violate the theory of relativity.