Calculate the angle of refraction
Online calculator and formulas for calculating the optical angle of refraction
Use this calculator to calculate the optical angle of refraction or the angle of incidence.
To calculate, select whether you want to calculate the angle of refraction or the angle of incidence, enter the required values, and then click the "Calculate" button.
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- \(n_1 \) - Refractive index of the first medium
- \(n_2 \) - Refractive index of the second medium
- \(θ_1 \) - Angle of incidence
- \(θ_2 \) - Angle of refraction
Formulas for the angle of refraction and incidence
To calculate the angle of refraction, Snell's law of refraction is used. This law describes how light is refracted at the interface between two media. The formula is:
\[n_1· sin(θ_1)=n_2· sin(θ_2)\]
Where:
- \(n_2 \) and \(n_2\) are the refractive indices of the two media
- \(θ_1\) is the angle of incidence (measured to the normal of the interface)
- \(θ_2\) is the angle of refraction
Rearrangement of the formula
Angle of refraction
\[n_1· sin(θ_1)=n_2· sin(θ_2)\]
\[ sin(θ_2)= \frac{n_1}{n_2} · sin(θ_1)\]
\[ θ_2 = arcsin\left(\frac{n_1}{n_2} · sin(θ_1)\right)\]
Angle of incidence
\[ θ_1 = arcsin\left(\frac{n_2}{n_1} · sin(θ_2)\right)\]
Example
In the example, it is assumed that light falls from air \(n_1= 1\) onto water \(n_2=1.33\) with an angle of incidence of 30°.
The angle of refraction is calculated as follows:
\[ sin(θ_2)= \frac{1}{1.33} · sin(30°)\]
\[ sin(θ_2)= \frac{1}{1.33} · 0.5≈0.3759\]
\[ θ_2= arcsin(0.3759)≈22.1°\]
Refractive indices for different materials
Material Refractive index (n) Vacuum 1.00000 Air (at 0°C) 1.00029 Water (20°C) 1.3330 Ethanol 1.3614 Olive oil ~1.47 Benzene 1,501 Quartz glass 1,458 Window glass ~1.52 Plexiglass (PMMA) 1.49 Crown glass (BK7) 1.5168 Flint glass (heavy) ~1.6 - 1.9 Diamond 2,417
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