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Formula 1 - Angles and Indices's banner
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Formula 1 - Angles and Indices

In this template, you will be able to use the first relationship of Snell's Law to determine the parameters stated below.

Formula


sin(θ1)sin(θ2) = n2n1\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{n_{2}}{n_{1}}

Refractive Indices

If you need to find the angles of incidence or refraction, provide the refractive index for each medium.
A list of refractive index is provided on this page: Refractive Index List

Read to find common medium refractive index values

Vacuum : 1
Air: 1.000293
Water (Room Temperature: 20 deg C approx.): 1.333
Ethanol: 1.36
Ice: 1.31
Acrylic: 1.49
Glass (Window): 1.52
Diamond: 2.419

Calculators

Angle of Refraction (given the indices)

Enter the refraction indices and angle of incidence to calculate the angle of refraction.
Formula:


Input:
The refractive index of medium 1,

n1
:1.333​

The refractive index of medium 2,

n2
:1​

The Angle of Incidence in degrees (

),

AOI
:20deg​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The Angle of Refraction (

or

AOR)
:27.12deg​


Angle of Incidence (given the indices)

Enter the refraction indices and angle of refraction to calculate the angle of incidence.
Formula:


Input:
The refractive index of medium 1,

n1
:1.333​

The refractive index of medium 2,

n2
:1.000293​

The Angle of Refraction in degrees (

) or

AOR
:50deg​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The Angle of Refraction in degrees (

or

AOI)
:35.09deg​


Refractive Index of Medium 1 (given the angles)

Enter the angle of refraction, the angle of incidence and refraction index of medium 2 to calculate the refraction index of medium 1.
Formula:


Input:
The Angle of Incidence in degrees (

) or

AOI
:50deg​

The Angle of Refraction in degrees (

) or

AOR
:20deg​

The refractive Index of medium 2,

n2 (1)
:1.000293​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The refractive index of medium 1,

n1 (2)
:0.446606​


Refractive Index of Medium 2 (given the angles)

Enter the angle of refraction, the angle of incidence and refraction index of medium 1 to calculate the refraction index of medium 1.
Formula:


Input:
The Angle of Incidence in degrees (

E=mc^2
) or

AOI (1)
:50deg​

The Angle of Refraction in degrees (

) or

AOR (2)
:20deg​

The refractive index of medium 1,

n1 (3)
:1.000293​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The refractive index of medium 2,

n2 (3)
:2.24042​


Critical Angle (using the indices)

When the AOR value in the "Finding Angle of Refraction" section shows "NaN", it means that the angle of incidence is greater than the critical angle and the wave now undergoes internal reflection rather than refraction.
Formula:


Input:
The refractive index of medium 1,

n1
:1.333​

The refractive index of medium 2,

n2
:1​

Output:
Using the formula denoted above, we can substitute the inputs to get:
Critical Angle,

or

CA
:48.61deg​


Velocity of the waves in each medium (using the indices)

Enter the indices and use the relationship on the left to find

and

. The variable

represents the speed of light.
Formula:


Input:
The refractive index of medium 1,

n1
:1​

The refractive index of medium 2,

n2
:1​

Speed of light through vacuum in m/s,

c
:300000000m/s​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The velocity of the wave in m/s in medium 1,

v1
:3.0E8m/s​

The velocity of the wave in m/s medium 2,

v2
:3.0E8m/s​


Wavelength of the waves in each medium (using the indices)

Enter the indices and use the relationship on the left to find

and

. Before you begin, ensure you know the nature of the wave since the

value represents the wavelength of wave in vacuum. But all waves have different wavelengths in vacuum. (For example,

of red light in vacuum is approx. 700 nm).
Formula:


Input:
The refractive index of medium 1,

n1
:1​

The refractive index of medium 2,

n2
:1​

The wavelength of the wave in vacuum,

λ0
:600nm​

Output:
Using the formula denoted above, we can substitute the inputs to get:
The wavelength of the wave in medium 1,

λ1
:600.0nm​

The wavelength of the wave in medium 2,

λ2
:600.0nm​



Related Resources

The values required from your end depend on the calculator you use, but all calculators revolve around the following parameters:

. If another type of variable is provided, look at our other calculators:
  1. 
    
    - Formula 2 Calculator
  2. 
    
    - Formula 3 Calculator
If unsure of which calculator use refer to the main page for reference: Snell's Law Calculators.