The electromagnetic spectrum

Section: Waves  |  Syllabus: Cambridge AS Level Physics (9702)

The Electromagnetic Spectrum

Electromagnetic waves are transverse waves that can travel through a vacuum at the speed of light.

Key Definitions

Electromagnetic (EM) waves: Transverse waves consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave propagation. They require no medium and can travel through a vacuum. Speed of light in vacuum (c): The speed at which all electromagnetic waves travel in free space.
c = 3.00 × 10⁸ m s⁻¹

Core Principles

Properties Shared by All Electromagnetic Waves

  1. They are all transverse waves
  2. They all travel at the same speed c = 3.00 × 10⁸ m s⁻¹ in a vacuum
  3. They can all travel through a vacuum (no medium required)
  4. They all transfer energy
  5. They can all be reflected, refracted, diffracted, and exhibit interference
  6. They can all be polarised
  7. They all obey v = fλ (so in vacuum: c = fλ)
  8. They are produced by accelerating charges or energy transitions

Structure of an EM Wave

An electromagnetic wave consists of:

The Electromagnetic Spectrum

Listed in order of increasing frequency (and decreasing wavelength):

Region Approximate Wavelength Range Notes
Radio waves > 0.1 m (10⁻¹ m) Longest wavelength, lowest frequency
Microwaves 0.1 m to 1 mm (10⁻¹ to 10⁻³ m) Used in cooking, communications
Infrared (IR) 1 mm to 700 nm (10⁻³ to 7 × 10⁻⁷ m) Heat radiation
Visible light 700 nm to 400 nm Only region visible to human eye
Ultraviolet (UV) 400 nm to 10 nm (4 × 10⁻⁷ to 10⁻⁸ m) Causes sunburn
X-rays 10 nm to 0.01 nm (10⁻⁸ to 10⁻¹¹ m) Medical imaging
Gamma rays (γ-rays) < 0.01 nm (< 10⁻¹¹ m) Shortest wavelength, highest frequency
FIG 7.6: The Electromagnetic Spectrum

Show the complete electromagnetic spectrum as a continuous band, ordered by wavelength (decreasing from left to right) or frequency (increasing from left to right). Label all regions: radio waves, microwaves, infrared, visible light (expanded to show colours ROYGBIV), ultraviolet, X-rays, gamma rays. Include approximate wavelength ranges and indicate the visible light region (400-700 nm) with its colour spectrum.

Memory Aid

(Decreasing wavelength): Runny Mashed Instant Vegetables Usually X-tremely Gross

(Radio, Microwave, Infrared, Visible, Ultraviolet, X-rays, Gamma)

Visible Light

The visible spectrum ranges from 400 nm (violet) to 700 nm (red).

Within visible light (increasing wavelength):

Memory Aid

Richard Of York Gave Battle In Vain

(Red, Orange, Yellow, Green, Blue, Indigo, Violet-decreasing wavelength)

Wave Equation for EM Waves

In a vacuum or free space:

c = fλ

where:

Since c is constant, frequency and wavelength are inversely proportional:

Concept Insight: EM Wave Production

All electromagnetic waves originate from accelerating electric charges or from electron transitions between energy levels:

Key Point

All EM waves travel at c in a vacuum because they are self-propagating disturbances in electric and magnetic fields-they don't require a medium.

Worked Examples

Worked Example 1: Calculating Frequency

Question: Calculate the frequency of green light with wavelength 550 nm.

Solution

Convert wavelength: λ = 550 nm = 550 × 10⁻⁹ m = 5.50 × 10⁻⁷ m

Using c = fλ:

f = (c/λ) = 3.00 × 10^85.50 × 10^-7 = 5.45 × 10^14 Hz

Worked Example 2: Calculating Wavelength

Question: A radio station broadcasts at a frequency of 98.5 MHz. Calculate the wavelength.

Solution

Convert frequency: f = 98.5 MHz = 98.5 × 10⁶ Hz = 9.85 × 10⁷ Hz

Using c = fλ:

λ = (c/f) = (3.00 × 10^8/9.85 × 10^7) = 3.05 m

Worked Example 3: Identifying EM Region

Question: An electromagnetic wave has a wavelength of 2.5 × 10⁻⁶ m. Identify the region of the EM spectrum and calculate its frequency.

Solution

λ = 2.5 × 10⁻⁶ m = 2.5 μm = 2500 nm

This is longer than visible light (700 nm) but shorter than microwaves. This is infrared radiation.

Frequency:

f = (c/λ) = 3.00 × 10^82.5 × 10^-6 = 1.2 × 10^14 Hz

Worked Example 4: Comparing Wavelengths

Question: How many times longer is the wavelength of a 100 MHz FM radio wave compared to visible red light (λ = 700 nm)?

Solution

Radio wavelength: λ = c/f = (3.00 × 10⁸)/(100 × 10⁶) = 3.0 m

Red light wavelength: λ = 700 nm = 700 × 10⁻⁹ m = 7.0 × 10⁻⁷ m

Ratio = 3.0 / (7.0 × 10⁻⁷) = 4.3 × 10⁶ times longer

Common Mistakes

Avoid These Errors
  1. Thinking different EM waves have different speeds in vacuum: All EM waves travel at c = 3.00 × 10⁸ m s⁻¹ in vacuum. Speed only changes when passing through a medium.
  2. Confusing wavelength ranges: Learn the approximate order of magnitude for each region. Visible light is around 10⁻⁷ m (hundreds of nanometres).
  3. Wrong direction of spectrum ordering: Higher frequency = shorter wavelength = more energetic (radio → gamma).
  4. Forgetting visible range limits: Visible light is 400–700 nm. Memorise these values.
  5. Unit errors: Be careful with nm, μm, and m conversions:
    • 1 nm = 10⁻⁹ m
    • 1 μm = 10⁻⁶ m
  6. Thinking EM waves are longitudinal: All EM waves are transverse-this is essential for polarisation.

Quick Concept-Check Questions

  1. What property do all electromagnetic waves share regarding their speed in a vacuum?
  2. What is the approximate wavelength range for visible light?
  3. Which has a higher frequency: X-rays or microwaves?
  4. Calculate the wavelength of a gamma ray with frequency 3.0 × 10²⁰ Hz.
  5. What type of electromagnetic wave has a wavelength of approximately 1 cm?

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