AcademyLight Propagation
Academy
Nature of Light
Level 1 - Physics topic page in Light Propagation.
Principle
Light is an electromagnetic wave. In vacuum it travels at speed \(c\), and its frequency, wavelength, and speed are related by the wave equation.
Notation
\(c\)
speed of light in vacuum
\(\mathrm{m\,s^{-1}}\)
\(v\)
speed of light in a material
\(\mathrm{m\,s^{-1}}\)
\(f\)
frequency
\(\mathrm{Hz}\)
\(\lambda\)
wavelength
\(\mathrm{m}\)
\(n\)
refractive index
\(\vec E\)
electric field in the light wave
\(\mathrm{V\,m^{-1}}\)
\(\vec B\)
magnetic field in the light wave
\(\mathrm{T}\)
Method
Derivation 1: Connect speed, frequency, and wavelength
Any periodic wave moves one wavelength in one period.
Wave speed
\[v=f\lambda\]
Vacuum light
\[c=f\lambda_0\]
Derivation 2: Use refractive index
The refractive index compares light speed in vacuum with light speed in a material.
Refractive index
\[n=\frac{c}{v}\]
Speed in a material
\[v=\frac{c}{n}\]
Derivation 3: Keep frequency fixed at a boundary
When light crosses from one medium into another, its frequency is set by the source and stays the same. Speed and wavelength change together.
Same frequency
\[f_1=f_2\]
Wavelength in material
\[\lambda=\frac{v}{f}=\frac{\lambda_0}{n}\]
Rules
Wave equation
\[v=f\lambda\]
Vacuum speed
\[c=3.00\times10^8\,\mathrm{m\,s^{-1}}\]
Refractive index
\[n=\frac{c}{v}\]
Material wavelength
\[\lambda=\frac{\lambda_0}{n}\]
Examples
Question
Light has wavelength
\[600\,\mathrm{nm}\]
in vacuum. Find its frequency.Answer
\[f=\frac{c}{\lambda}=\frac{3.00\times10^8}{600\times10^{-9}}=5.00\times10^{14}\,\mathrm{Hz}\]
Checks
- Frequency does not change when light crosses a boundary.
- Wavelength is shorter in a material with \(n>1\).
- The electromagnetic wave model explains reflection, refraction, interference, diffraction, and polarization.
- Ray and photon models are useful in other contexts, but this section mainly uses the wave model.