4.4.2(a)-(c) - Electromagnetic spectrum and polarisation

4.4.2(a)-(c) - Electromagnetic spectrum and polarisation

Electromagnetic waves include radio waves, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. In this lesson you will learn what all electromagnetic waves have in common, how to place the main regions of the spectrum on a wavelength scale, and how polarisation shows that electromagnetic waves are transverse. The aim is not to memorise every boundary perfectly, but to become fluent with the order and the powers of ten.

Electromagnetic Wave Model

An electromagnetic wave is a progressive wave made from oscillating electric and magnetic fields. Unlike a wave on a string or a sound wave in air, it does not need a material medium: it can travel through a vacuum.

Electromagnetic Wave

An electromagnetic wave is a transverse wave consisting of oscillating electric and magnetic fields that are perpendicular to each other and perpendicular to the direction of travel.

For OCR, the most important common properties are:

  • electromagnetic waves are transverse;
  • they can travel through a vacuum;
  • in a vacuum they all travel at the same speed, c=3.00×108 m s−1c = 3.00 \times 10^8\ \mathrm{m}\,\mathrm{s}^{-1};
  • they can transfer energy from one place to another;
  • they are described by wavelength λ\lambda, frequency ff and speed vv, as for other progressive waves.

The wave equation from the previous wave lesson still applies:

Wave equation for electromagnetic waves

c=fλc = f\lambda

Here cc is the speed of electromagnetic waves in a vacuum, ff is frequency in hertz, and λ\lambda is wavelength in metres. This equation means that, in a vacuum, a shorter wavelength goes with a higher frequency.

Do not confuse the wavelength with the direction of oscillation. The wavelength is a distance along the direction of travel; the electric and magnetic field oscillations are sideways to the direction of travel.

For a plane electromagnetic wave in a vacuum, the electric and magnetic fields oscillate in phase and have the same frequency and wavelength. Both are perpendicular to the direction of propagation and to each other. The sinusoidal curves represent field values at positions along the beam; they are not paths followed by particles of a medium.

[DIAGRAM: asset_slug: 4_04_2a_electromagnetic_spectrum_and_polarisation__diagram_01; caption: Electric and magnetic fields have the same phase and wavelength, with mutually perpendicular field and propagation directions.; description: Aligned field graphs have identical phase and wavelength. Electric field, magnetic field and propagation form mutually perpendicular directions; their relative plotted scales are not physical equal units.]
Electric and magnetic fields have the same phase and wavelength, with mutually perpendicular field and propagation directions.

Spectrum Order and Wavelengths

The electromagnetic spectrum is one continuous family. The names are labels for broad regions, not separate types of substance.

From longest wavelength to shortest wavelength, the principal regions are:

  1. radio waves
  2. microwaves
  3. infrared
  4. visible light
  5. ultraviolet
  6. X-rays
  7. gamma rays

Approximate wavelength orders are enough for this lesson:

RegionRepresentative wavelength scale
radio100 m10^{0}\,\mathrm{m} and longer, often metres to kilometres
microwaveabout 10−310^{-3} to 10−1 m10^{-1}\ \mathrm{m}
infraredabout 10−610^{-6} to 10−3 m10^{-3}\ \mathrm{m}
visible lightabout 4×10−74 \times 10^{-7} to 7×10−7 m7 \times 10^{-7}\ \mathrm{m}
ultravioletabout 10−810^{-8} to 10−7 m10^{-7}\ \mathrm{m}
X-raysabout 10−1110^{-11} to 10−8 m10^{-8}\ \mathrm{m}
gamma raysabout 10−12 m10^{-12}\ \mathrm{m} or shorter

The exact edges vary a little between sources and applications. OCR's phrase "orders of magnitude" is the clue: you should know the scale and sequence, not a long list of sharp borders.

Worked example: identifying regions from wavelength

A radiation has wavelength 5.5×10−7 m5.5 \times 10^{-7}\ \mathrm{m}.

This is between 4×10−7 m4 \times 10^{-7}\ \mathrm{m} and 7×10−7 m7 \times 10^{-7}\ \mathrm{m}, so it is visible light.

A radiation has wavelength 3.0×10−2 m3.0 \times 10^{-2}\ \mathrm{m}.

This is 0.030 m0.030\,\mathrm{m}, or 3 cm3\,\mathrm{cm}, so it is in the microwave region.

[DIAGRAM: asset_slug: 4_04_2a_electromagnetic_spectrum_and_polarisation__diagram_02; caption: Representative wavelengths decrease from radio waves to gamma rays on a logarithmic scale. Visible light spans about 400–700 nm.; description: A descending logarithmic wavelength axis places representative radio, microwave, infrared, visible, ultraviolet, X-ray and gamma wavelengths. Visible light occupies about 400–700 nm; named boundaries are approximate.]
Representative wavelengths decrease from radio waves to gamma rays on a logarithmic scale. Visible light spans about 400–700 nm.

Using Orders of Magnitude

An order of magnitude is a factor of about 10. If two wavelengths differ by a factor of 10610^{6}, they differ by six orders of magnitude.

This skill is useful because the electromagnetic spectrum covers a huge range. A radio wavelength might be metres long, while a gamma-ray wavelength may be on atomic or nuclear length scales. A normal linear scale would be almost useless, so physicists often think in powers of ten.

Worked example: comparing visible light and gamma rays

Take a typical visible wavelength as:

λvisible=5.0×10−7 m\lambda_{\text{visible}} = 5.0\times 10^{-7}\ \text{m}

Take a typical gamma-ray wavelength as:

λγ=1.0×10−12 m\lambda_{\gamma} = 1.0\times 10^{-12}\ \text{m}

The ratio is:

5.0×10−71.0×10−12=5.0×105\frac{5.0\times 10^{-7}}{1.0\times 10^{-12}} = 5.0\times 10^5

This is close to 10610^{6}, so the visible-light wavelength is about six orders of magnitude larger than the gamma-ray wavelength.

Worked example: linking wavelength and frequency

In a vacuum, a wave with wavelength 0.10 m0.10\,\mathrm{m} has frequency:

f=cλf = \frac{c}{\lambda}

Continue this lesson.

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