IMAT Physics · Oscillations and Waves

The Electromagnetic Spectrum, Diffraction and Interference

Light is one band of a spectrum of electromagnetic waves that all travel at c in a vacuum; like every wave they reflect, refract, diffract and interfere.

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Why this matters

The one past question here is from the 2026 ministry paper and asked what makes two waves coherent. The rest of the page is syllabus that has not been tested yet.

Concept 1 of 3: The electromagnetic spectrum: order, wavelengths and uses

Radio waves, light and X-rays are the same kind of wave: oscillating electric and magnetic fields. They differ only in wavelength, and so in frequency and in the energy each photon carries. Short wavelength means high frequency and high energy, which is why gamma rays, X-rays and ultraviolet can damage cells.

Definition

All electromagnetic waves are transverse, need no medium, and travel at $c = 3.00 \times 10^8\ \text{m/s}$ in a vacuum, so $c = f\lambda$ .
In order of increasing wavelength (decreasing frequency): gamma, X-rays, ultraviolet, visible, infrared, microwaves, radio.
Visible light runs from violet (about 400 nm) to red (about 700 nm).
Photon energy $E = hf$ rises with frequency. Gamma, X-rays and high-energy ultraviolet are ionising.

Region	Typical wavelength	Use or source
Gamma rays	Below about $10^{-11}\ \text{m}$	Radiotherapy, sterilising medical equipment, radioactive decay
X-rays	About $10^{-11}$ to $10^{-8}\ \text{m}$	Imaging bones and teeth, CT scans
Ultraviolet	About 10 nm to 400 nm	Sterilising water, vitamin D in the skin, sunburn
Visible light	About 400 nm to 700 nm	Sight, optical fibres, photosynthesis
Infrared	About 700 nm to 1 mm	Heat radiation, remote controls, thermal cameras
Microwaves	About 1 mm to 30 cm	Microwave ovens, mobile phones, radar
Radio waves	Above about 30 cm	Radio and TV broadcasting, MRI scanners

Practice this conceptself-check · 4 quick reps

All electromagnetic waves have the same speed in a vacuum

Gamma rays and radio waves both travel at

3.00 \times 10^8\ \text{m/s}

in a vacuum. What differs is the frequency and wavelength. Radio waves are not sound waves: they are electromagnetic and cross a vacuum.

Concept 2 of 3: Reflection, refraction, diffraction and polarisation of waves

Every kind of wave, from ripples to light, does the same few things at a boundary or a gap. It bounces back, it bends as its speed changes, and it spreads round edges. How much it spreads depends on how the gap compares with its wavelength, which is why sound bends round a doorway but light hardly does.

Definition

Reflection: the angle of incidence equals the angle of reflection, both measured from the normal.
Refraction: a change of speed at a boundary bends the wave if it arrives at an angle. Frequency stays; speed and wavelength change.
Diffraction: spreading after passing through a gap or round an edge. It is strongest when the gap is about one wavelength wide.
Polarisation: restricting the vibrations to one plane. Only transverse waves can be polarised, so sound cannot.

Behaviour	What happens	What changes	Example
Reflection	The wave bounces off a boundary	Direction only	An echo; an image in a mirror
Refraction	The wave bends as it changes speed entering a new medium	Speed, wavelength and direction; not frequency	A straw looking bent in water
Diffraction	The wave spreads out after a gap or an edge	Direction spreads; speed, frequency and wavelength stay	Hearing a voice round a corner
Polarisation	Vibrations are limited to one plane	Plane of vibration	Polarising sunglasses cutting glare

Practice this conceptself-check · 3 quick reps

Diffraction does not change the wavelength

After a gap the wave spreads out, but its speed, frequency and wavelength are the same as before. Only refraction, a change of medium, changes the wavelength.

Concept 3 of 3: Superposition, coherence, interference and standing waves

When two waves meet, their displacements simply add. Crest on crest gives a bigger wave; crest on trough cancels. For the pattern of loud and quiet spots to stay put, the two sources must keep in step, with a phase difference that never changes. That is coherence. Two waves travelling in opposite directions along a string add up to a standing wave, with points that never move.

Definition

Superposition: where waves overlap, the resulting displacement is the sum of the separate displacements.
Two sources are coherent if they have the same frequency and a constant phase difference. Only coherent sources give a steady interference pattern. Equal amplitude is not required.
Path difference $\Delta$ from two coherent sources in phase: $\Delta = n\lambda$ gives constructive interference (loud, bright); $\Delta = (n + \tfrac{1}{2})\lambda$ gives destructive (quiet, dark).
A standing wave has nodes (no motion) and antinodes (largest motion). Neighbouring nodes are $\lambda/2$ apart.
On a string of length $L$ fixed at both ends, $L$ holds a whole number $n$ of half-wavelengths: $\lambda_n = 2L/n$ . The fundamental ( $n = 1$ ) has $\lambda = 2L$ .

Interference conditions and a string fixed at both ends

\Delta = n\lambda \ \text{(constructive)} \qquad \Delta = \left(n + \tfrac{1}{2}\right)\lambda \ \text{(destructive)} \qquad \lambda_n = \frac{2L}{n}

$\Delta$ path difference from the two sources, in m
$n$ a whole number (0, 1, 2, … for interference; 1, 2, 3, … for the string)
$\lambda$ wavelength, in m
$L$ length of the string, in m

Worked example

Two loudspeakers play the same 680 Hz tone in phase. Sound travels at 340 m/s. A listener is 4.00 m from one speaker and 4.75 m from the other. Is the sound loud or quiet there?

Practice this conceptself-check · 4 quick reps

Coherence is about phase, not amplitude or brightness

Two waves are coherent when their phase difference stays constant in time, which needs equal frequencies. A strong wave and a weak one can be perfectly coherent, and so can two radio or sound waves: coherence is about keeping in step.

Nodes are half a wavelength apart, not a whole one

In a standing wave each loop between neighbouring nodes is

\lambda/2

long. Counting a loop as a whole wavelength halves every wavelength you work out.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Superposition, coherence, interference and standing waves
Interference conditions and a string fixed at both ends
$\Delta = n\lambda \ \text{(constructive)} \qquad \Delta = \left(n + \tfrac{1}{2}\right)\lambda \ \text{(destructive)} \qquad \lambda_n = \frac{2L}{n}$

Reference tables (2)

The electromagnetic spectrum: order, wavelengths and uses7 rows

Region	Typical wavelength	Use or source
Gamma rays	Below about $10^{-11}\ \text{m}$	Radiotherapy, sterilising medical equipment, radioactive decay
X-rays	About $10^{-11}$ to $10^{-8}\ \text{m}$	Imaging bones and teeth, CT scans
Ultraviolet	About 10 nm to 400 nm	Sterilising water, vitamin D in the skin, sunburn
Visible light	About 400 nm to 700 nm	Sight, optical fibres, photosynthesis
Infrared	About 700 nm to 1 mm	Heat radiation, remote controls, thermal cameras
Microwaves	About 1 mm to 30 cm	Microwave ovens, mobile phones, radar
Radio waves	Above about 30 cm	Radio and TV broadcasting, MRI scanners

Reflection, refraction, diffraction and polarisation of waves4 rows

Behaviour	What happens	What changes	Example
Reflection	The wave bounces off a boundary	Direction only	An echo; an image in a mirror
Refraction	The wave bends as it changes speed entering a new medium	Speed, wavelength and direction; not frequency	A straw looking bent in water
Diffraction	The wave spreads out after a gap or an edge	Direction spreads; speed, frequency and wavelength stay	Hearing a voice round a corner
Polarisation	Vibrations are limited to one plane	Plane of vibration	Polarising sunglasses cutting glare

Watch out for (4)

All electromagnetic waves have the same speed in a vacuum
→ The electromagnetic spectrum: order, wavelengths and uses
Diffraction does not change the wavelength
→ Reflection, refraction, diffraction and polarisation of waves
Coherence is about phase, not amplitude or brightness
→ Superposition, coherence, interference and standing waves
Nodes are half a wavelength apart, not a whole one
→ Superposition, coherence, interference and standing waves

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