IGCSE Physics – Electromagnetic Spectrum3.3 Electromagnetic Spectrum
Objective
Know that the speed of electromagnetic waves in a vacuum is \$3.0 \times 10^{8}\ \text{m s}^{-1}\$ and is approximately the same in air.
Key Concepts
- Electromagnetic (EM) waves travel without a material medium.
- All EM waves travel at the same speed in vacuum: \$c = 3.0 \times 10^{8}\ \text{m s}^{-1}\$.
- In air, the speed differs by less than 0.03 % and can be taken as \$c\$ for most calculations.
- Relationship between speed, frequency and wavelength: \$c = \lambda\,f\$.
Electromagnetic Spectrum Overview
| Region | Typical Wavelength \$\lambda\$ (m) | Typical Frequency \$f\$ (Hz) | Uses / Examples |
|---|
| Radio | \$10^{-1}\$ to \$10^{3}\$ | \$10^{6}\$ to \$10^{9}\$ | Broadcasting, radar |
| Microwave | \$10^{-3}\$ to \$10^{-1}\$ | \$10^{9}\$ to \$10^{12}\$ | Cooking, satellite communication |
| Infrared | \$10^{-6}\$ to \$10^{-3}\$ | \$10^{12}\$ to \$10^{14}\$ | Heating, remote controls |
| Visible | \$4 \times 10^{-7}\$ to \$7 \times 10^{-7}\$ | \$4.3 \times 10^{14}\$ to \$7.5 \times 10^{14}\$ | Human vision |
| Ultraviolet | \$10^{-8}\$ to \$4 \times 10^{-7}\$ | \$7.5 \times 10^{14}\$ to \$3 \times 10^{16}\$ | Sterilisation, sunburn |
| X‑ray | \$10^{-11}\$ to \$10^{-8}\$ | \$3 \times 10^{16}\$ to \$3 \times 10^{19}\$ | Medical imaging |
| Gamma ray | \$<10^{-11}\$ | \$>3 \times 10^{19}\$ | Radioactive decay |
Calculations Using \$c = \lambda f\$
Example: Find the frequency of a radio wave with wavelength \$0.5\ \text{m}\$.
\$\$
f = \frac{c}{\lambda} = \frac{3.0 \times 10^{8}\ \text{m s}^{-1}}{0.5\ \text{m}} = 6.0 \times 10^{8}\ \text{Hz}
\$\$
Why the Speed is the Same in Air
- Air is a very low‑density medium; its refractive index \$n \approx 1.0003\$.
- The speed in a medium is \$v = \dfrac{c}{n}\$, so in air \$v \approx \dfrac{c}{1.0003} \approx 0.9997c\$.
- For most IGCSE calculations the difference is negligible, so we use \$c\$.
Suggested diagram: A spectrum chart showing the regions from radio waves to gamma rays with representative wavelengths and frequencies.
Common Exam Questions
- State the speed of light in vacuum and in air.
- Calculate the wavelength of a microwave with frequency \$2.4 \times 10^{9}\ \text{Hz}\$.
- Identify which part of the spectrum is used for television broadcasting.
Summary
- The speed of EM waves in vacuum is \$c = 3.0 \times 10^{8}\ \text{m s}^{-1}\$.
- In air the speed is essentially the same, differing by less than 0.03 %.
- All EM waves obey \$c = \lambda f\$, allowing conversion between wavelength and frequency.
- The electromagnetic spectrum covers a vast range of wavelengths and frequencies, each with practical applications.