Snell's Law Calculators

This law provides a formula to help calculate the relationship between the angles of incidence and refraction when a wave passes from one isotropic medium to another. Mediums are materials through which waves propagate, such as water, air, or glass. You will also be able to find the critical angle in each of the templates.
CalculatorsThis page will give an explanation to the formulas. If you want to access the calculations templates, click on the relevant one below! 
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sin(θ1)sin(θ2) = n2n1\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{n_{2}}{n_{1}}sin(θ2​)sin(θ1​)​ = n1​n2​​
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Formula 1 - Angles and Indices
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sin(θ1)sin(θ2) = v1v2\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{v_{1}}{v_{2}}sin(θ2​)sin(θ1​)​ = v2​v1​​
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Formula 2 - Angles and Velocities
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sin(θ1)sin(θ2) = λ1λ2\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{\lambda_{1}}{\lambda_{2}}sin(θ2​)sin(θ1​)​ = λ2​λ1​​
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Formula 3 - Angles and Wavelengths
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You can also look at finding Prism Refraction Angle, which can be found below:
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Prism Refraction Angle Calculator
ExplanationBackgroundWhen the wave passes between a pair of media, it refracts (bends). This phenomenon occurs because its speed and wavelength change when a wave enters a different medium. Due to this change, the wave bends one of two ways. If the speed decreases, the wave bends towards the normal media boundary, and if the speed increases, the wave bends towards the boundary (away from the normal). The properties of the medium determine the change in speed. 
LawSnell’s law states that, for a given pair of media, the ratio of the sines of angle of incidence (﻿θ1​
) and the angle of refraction (﻿θ2​
) is equal to the ratio of refractive indices of medium 1 to medium 2 (﻿n2​n1​​
) and is also equal to the ratio of the wave speed in medium 2 to medium 1 (﻿v1​v2​​
) and is also equal to the ratio of wavelength in medium 1 to medium 2 (﻿λ2​λ1​​
)
We can make a collective relationship for the different parameters from the three formulas (as shown above). This relationship can then be used to find dependent values. 
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sin(θ1)sin(θ2) = n2n1 = v1v2 = λ1λ2\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{n_{2}}{n_{1}}\ =\ \cfrac{v_{1}}{v_{2}}\ =\ \cfrac{\lambda_{1}}{\lambda_{2}}sin(θ2​)sin(θ1​)​ = n1​n2​​ = v2​v1​​ = λ2​λ1​​
Parameters﻿﻿θ1​
 : Angle of Incidence is the angle between the line normal to the media boundary and the incoming wave through medium 1.
﻿﻿θ2​
 : Angle of Refraction is the angle between the line normal to the media boundary and the outgoing wave through medium 2.
﻿﻿n1​
 : Refractive Index of medium 1
﻿﻿n2​
 : Refractive Index of medium 2 
﻿﻿v1​:
 Wave speed in medium 1
﻿﻿v2​
 : Wave Speed in medium 2
﻿﻿λ1​
 : Wavelength of wave in medium 1
﻿﻿λ2​
 : Wavelength of wave in medium 2
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Relationship between parameters
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Critical AngleIt is the Angle of Incidence, when the Angle of Refraction is equal to 90 degrees with respect to the normal to the media boundary, Hence, the refracted ray is parallel to the media boundary.
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Critical Angle
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This angle is crucial to note since any wave incident at the boundary at an angle greater than this "Critical Angle" will undergo "Total Internal Reflection" instead of Refraction, and Snell's Law is no longer applicable to this wave.
To calculate the critical angle, the following steps can be followed:
Set ﻿sin(θ2​) = 90 deg
 as this is a known value.
Using Snell's Law, rearrange to get the equation: ﻿θ1​ = sin−1(xn​xm​sin(θ2​)​)
, where the variable ﻿x
 corresponds to either the refractive index, speed or wavelength (﻿n,v,λ
).
Calculate the Critical Angle denoted by the Angle of Incidence (﻿θ1​
).
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Velocity using the Refractive IndexIf both indexes are known, the velocity of a wave through a medium can be easily derived using the formula on the left. 
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vm = cnmv_{m}\ =\ \cfrac{c}{n_{m}}vm​ = nm​c​
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Wavelength using the Refractive IndexThe wavelength of a wave through a medium can be easily derived using the formula on the left if both indexes are known. 
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λm = λ0nm\lambda_{m}\ =\ \cfrac{\lambda_{0}}{n_{m}}λm​ = nm​λ0​​
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In both of the above cases, if the indexes are unknown, but any other values are given or found, use any relationship from the equation below to find the missing variable.
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n2n1 = v1v2 = λ1λ2\cfrac{n_{2}}{n_{1}}\ =\ \cfrac{v_{1}}{v_{2}}\ =\  \cfrac{\lambda_{1}}{\lambda_{2}}n1​n2​​ = v2​v1​​ = λ2​λ1​​
SummaryThis template provides a method to calculate any parameter that is related to Snell's Law using one of three formulas. Furthermore, you can find the critical angle and there is also insight regarding refraction within a prism. 
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