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Formula 2 - Angles and Velocities's banner
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Formula 2 - Angles and Velocities

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

Formula:


sin(θ1)sin(θ2) = v1v2\cfrac{sin(\theta_{1})}{sin(\theta_{2})}\ =\ \cfrac{v_{1}}{v_{2}}

Calculators

Angle of Refraction (given the velocities)

Enter the velocity through medium 1 and the velocity through medium 2 to find the angle of refraction.
Formula:


Input:
Velocity of the wave in m/s in medium 1,

v1
:100m/s​

Velocity of the wave in m/s in medium 2,

v2
:133m/s​

Angle of Incidence in degrees

or

AOI
:20deg​

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

or

AOR
:27.06deg​


Angle of Incidence (given the velocities)

Velocity of wave in Medium 1 (given the angles)

Velocity of wave in Medium 2 (given the angles)

Critical Angle (using the velocities)

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:
Velocity of the wave in m/s through medium 1,

v1
:100m/s​

Velocity of the wave in m/s through medium 2,

v2
:133m/s​

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

or

CA
:48.75deg​



Refractive Indices of the mediums and wavelength of the waves in each medium (given the velocities)

Enter the velocities and use the first relationship on the left to find

and

. After finding the indices, those values can then be used to find the wavelength values using the second relationship on the left column.
Before you try to find the wavelength, 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).
The variable

represents the speed of light.
Formula 1:


Formula 2:


Input:
Velocity of wave in m/s in medium 1,

v1 (1)
:300000000m/s​

Velocity of wave in m/s in medium 2,

v2 (1)
:300000000m/s​

Speed of light through vacuum,

c
:300000000m/s​

Wavelength of the wave through vacuum,

λ0
:600nm​
Output:
Using the formula denoted above, we can substitute the inputs to get:
Using Formula 1:
Refractive index of medium 1,

n1
:1.0​

Refractive index of medium 2,

n2
:1.0​

Using Formula 2:
Wavelength of wave in medium 1,

λ1
:600.0nm​

Wavelength of 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 1 Calculator
  2. 
    
    - Formula 3 Calculator
If unsure of which calculator use refer to the main page for reference: Snell's Law Calculators