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Snell's Law Calculator

Select the parameter and enter required ones. The tool will find its value using Snell's law, with the steps shown.

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The Snell's law calculator measures the angle of refraction of light from one medium to another. You can find the angle of refraction, angle of incidence, and ratio of refractive indexes by our Snell law calculator.

The Snell's Law:

This law states that: “A relationship between the angle of refraction and incidence, when light is entering from one medium to another” The angle of refraction depends upon the refractive index of a particular medium. Snell's law calculation describes the working mechanism of refraction of light in various media. The wavelength of the light is different in various media like vacuum, water, ice, and air. This is why the light bends towards or away from the normal of two medium boundaries. Snell's law calculator determines the refractive index of light on the basis of the speed of light in a certain medium. If the speed of light changes then the refraction angle also changes as it depends on the wavelength or the speed of light in a certain medium.

Snell's Law Equation:

The refraction angle depends on the wavelength of light in both media. The Snell's law equation is given as follows: n_1 sin θ_1 = n_2 sin θ_2 Where
  • n_1 & n_2 =  the refractive index of medium 1 and medium 2, respectively.
  • θ_1 =  angle of incidence
  • θ_2 = angle of refraction
You can express the Snell’s law formula in the following form: Sin i / Sin r = μ Here,
  •  i” = angle of incidence
  • r” =  angle of refraction
  • μ” = ratio of the  refractive index of two media
The Snell law calculator assists to determine the behavior of light when traveling from incident to refracted medium. The Snells law equation tells us the light's bending when entering from one medium like a vacuum to water.

Practical Example:

Calculate the refractive index of the ray of light from air to water by the Snell law formula. The refractive index of air and water at 20 degrees are 1.000293 and 1.333 respectively. The angle of the incidence ray is around 30 degrees when entering from air to water.

Given:

The refractive index of air = n_1 = 1.000293 The refractive index of air = n_1 = 1.333 Angle of Incidence (θ_2) =  30 = 0.523599

Solution:

The Snell law formula for the angle of refraction from one medium to another is Snell law formula = θ1= sin-1((n₁ * sin(θ2)) / n₂) Put values into Snell law equation: The refractive angle = θ₁ = sin-1((1.000293 * sin(0.523599)) / 1.333) The refractive angle = θ₁ = 22.036919 The Snells law calculator describes the change in the path or the bending of light rays when entering from one medium to another.

Chart of Refractive Index of Various Mediums:

The Snell's law calculation of refraction of various media is given below:
Medium Refractive index
Air 1.000293
Carbon Dioxide 1.000449
Hydrogen 1.000132
Methane 1.000444
Nitrogen 1.000298
Oxygen 1.000271
Milk 1.35
Olive Oil 1.47
Water 1.333
Glass 1.5 a 1.62
Diamond 2.417
Polycarbonate 1.59

Working of the Snell’s Law Calculator?

The method of using the Snells law calculator is given below: Input:
  • Enter the refraction index of the first and second medium
  • Enter the angle of incidence
  • Tap Calculate
Output:
  • The refractive index of light
  • The angle of incidence & refraction 

References:

From the source Wikipedia: Snell's law, History  From the source brilliant.org: The refraction, Snell law formula
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