# A-level Physics/Electrons, Waves and Photons/Electromagnetic waves

## Structure

Electromagnetic (EM) waves are transverse waves that carry energy. This means the light can be polarised like all other transverse waves. Depending on the amount of energy, the waves create the electromagnetic spectrum, comprising (from longest to shortest wavelengths) radio, microwave, infra-red, visible light, ultraviolet, X-ray, gamma ray. Commonly referred to as EM "Radiation," these waves have wavelengths ranging from several thousand kilometres (${\displaystyle \geq 10^{5}}$ m) to sub-picometres (${\displaystyle \leq 10^{-12}}$ m).

The wave is actually made up of two components which are perpendicular to the direction of the wave. EM radiation can be thought of as particles (the photon) or waves, which is commonly referred to as the "wave particle duality"

## The Speed of Light

All electromagnetic waves travel at the same speed (in a vacuum), and that is the universal constant known as the "speed of light," most often abbreviated by the lower-case letter "c".

The speed of light is (exactly):
c = 299 792 458 ${\displaystyle m/s}$ or
c = 983 571 056 ${\displaystyle ft/s}$

## Visible Light

In the middle of the electromagnetic spectrum is visible light, i.e., the range that the human eye has evolved to observe. The following is a chart of the wavelengths of visible light.

  Colour                  Wavelength (m)
near ultraviolet          3.0 e -7
shortest visible blue     4.0 e -7
blue                      4.6 e -7
green                     5.4 e -7
yellow                    5.9 e -7
orange                    6.1 e -7
longest visible red       7.6 e -7
near infra-red            1.0 e -6
(Table 9.1, Griffiths)


## Useful Equations

To find out the energy of a particular EM wave, or its frequency one can use the several forms of the Einstein Equation.

First, to determine an EM wave frequency, ${\displaystyle \nu }$ from its wavelength, ${\displaystyle \lambda }$. The wavelength multiplied by the frequency is always a constant value: the speed of light, ${\displaystyle c}$. Hence,

(1) c = ${\displaystyle \nu \lambda }$,


so you can find the frequency from the wavelength, or vice versa from simply manipulating this relationship.

Next, to determine the energy from a smallest quantity of EM wave (photon). Here, we must introduce another universal quantity known as "Planck's Constant," most commonly abbreviated by a lower-case "h." Planck's constant is

h = 6.626068 e -34 ${\displaystyle m^{2}kg/s}$.


With this in place we can use the "Planck Equation," which provides a relationship between the frequency, ${\displaystyle \nu }$ and energy ${\displaystyle E}$ of a photon. The relation is as follows:

(2) E = h ${\displaystyle \nu }$.


Now, if we only have the wavelength with which to start, we can manipulate equation (1) to get what we need.

(1) c = ${\displaystyle \nu \lambda }$,
${\displaystyle \nu =c/\lambda }$,

(2) E = h c / ${\displaystyle \lambda }$.


## References

(In order of Mathematical/Material Depth)

Halliday D.; Resnick R.; Walker J.; Fundamentals of Physics, Part 4: Chapters 34 - 38. 6th ed. John Wiley & Sons, Inc., 2003. Chapter 34.

Griffiths, David J. Introduction to Electrodynamics. 3rd ed. Upper Saddle River, NJ: Prentice-Hall, Inc., 1999. Chapter 9, p364-411.

Rybicki, G.; Lightman, A. Radiative Processes in Astrophysics. Wiley-Interscience, 1985.