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Wave Superposition
Last Update: October 20, 2024
Introduction
Electromagnetic waves produced by different sources will combine in a process called superposition.
In this post, we’ll describe basic wave superposition and why light slows down when entering a medium with a higher refractive index.
Also refer to my posts:
- Refractive Geometric Optics
- Understand Your Eyes which has links to my other eye and optics related articles.
Electromagnetic Wave Superposition
Electromagnetic Waves are additive; a concept known as Superposition.
Consider the picture below showing three scenarios for superposition.
Picture_Superposition of Waves
Here is a description of each graph shown in picture Above:
1. Top Graph (Destructive Interference)
This graph illustrates destructive interference, where two similar waves are 180 degrees apart and completely out of phase.
Because the crests of one wave align with the troughs of the other, the two waves completely cancel each other out.
As a result, the amplitude of the combined Resultant Wave 3 is zero.
2. Middle Graph (Partial Interference)
This graph demonstrates two similar waves that are partially out of phase with each other.
Because they are neither completely aligned nor completely inverted, they combine to form an intermediate wave.
The resulting amplitude of Wave 3 falls somewhere between zero and twice the amplitude of either individual wave.
3. Bottom Graph (Constructive Interference)
This graph depicts constructive interference, which occurs when two waves are 0 or 360 degrees apart and in-phase.
Because their peaks and troughs align perfectly, they reinforce one another when combined.
Consequently, the amplitude of the resulting Wave 3 is doubled, measuring twice as large as Wave 1 or Wave 2.
If the wavelengths are different, they will still be additive.
But the resultant wave won’t necessarily be symmetrically shaped.
Even waves moving at different speeds (remember velocity = frequency x wavelength) are additive.
Why Light Slows Down When it Enters a Refractive Medium
When light enters a higher refractive medium (e.g from air to water or glass), it interacts with the atoms and associated electrons in the material.
The electrons of the medium begin to oscillate due to the light waves.
This oscillation creates separate oscillating electric fields (and therefore “new waves”).
- Superposition occurs among the light waves and the waves from the oscillating medium electrons.
- The resultant waves are always slower moving.
- This is why the light slows down in the medium.
- This slowing down is influenced by the properties of the material, such as the density and arrangement of atoms and molecules.
- The index of refraction is a measure of how much a material slows down light compared to its speed in a vacuum.
- Index of Refraction = n = (speed of light in a vacuum)/(speed of light in the material) and will always be > 1 for any material
- For air, n is slightly larger than 1 (n = 1.0003) since the speed of light in air is slightly less than the speed of light in a vacuum.
- As soon as the light exits the medium, the interference from the medium oscillating electrons ends (i.e. superposition effect ends).
- So, the light exiting the material resumes the speed it had before entering the medium (e.g. light going from air to glass to air)
In summary, the interaction between light and electrons in a refractive medium leads to the slowing down of light waves.
As soon as the medium electron wave interference ends (as the light exits the medium), the speed of light in air resumes.
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