Physics 9702 · Paper 2

The Electromagnetic Spectrum

Electromagnetic (EM) waves are transverse waves that all travel at the same speed $c = 3.0\times10^8\text{ m s}^{-1}$ in a vacuum.
They form one continuous family, from radio waves to gamma rays, differing only in wavelength and frequency.

One family, one speed

An EM wave is a linked electric and magnetic field, each oscillating at right angles to the other and to the direction of travel. That is why EM waves are transverse.

An electromagnetic wave is a linked pair of fields. The electric field (red) oscillates up and down; the magnetic field (blue) oscillates in the plane at right angles to it. Both are at right angles to the direction of travel, so all EM waves are transverse.

In a vacuum they all move at $c$ , linked to frequency and wavelength by $c = f\lambda$ (the wave equation again).
Visible light is a thin band from about 400 nm (violet) to 700 nm (red).

The whole electromagnetic family on one scale. They all travel at the same speed in a vacuum; only the wavelength (and frequency) change. Visible light is the thin band from about 400 nm to 700 nm.

Band (increasing wavelength →)	Rough wavelength range
γ-rays	10⁻¹⁶ to 10⁻¹⁰ m
X-rays	10⁻¹³ to 10⁻⁸ m
ultraviolet	10⁻⁸ to 4 × 10⁻⁷ m
visible	4 × 10⁻⁷ to 7 × 10⁻⁷ m
infrared	7 × 10⁻⁷ to 10⁻³ m
microwaves	10⁻³ to 10⁻¹ m
radio waves	10⁻¹ to > 10⁶ m

Learn the order by increasing wavelength: γ-rays, X-rays, ultraviolet, visible, infrared, microwaves, radio waves. They all share one speed in a vacuum.

Using c = fλ and the ranges

Worked example

Frequency of green light

Green light has a wavelength of about 550 nm in a vacuum. Find its frequency.

$\lambda = 550\text{ nm} = 5.5\times10^{-7}\text{ m}$ .
$f = \dfrac{c}{\lambda} = \dfrac{3.0\times10^8}{5.5\times10^{-7}} \approx 5.5\times10^{14}\text{ Hz}$ .

Answer

f \approx 5.5\times10^{14}\text{ Hz}

Why the wavelength changes in glass but the colour does not

When light enters glass it slows down, but the source still sends the same number of waves per second, so the frequency stays the same. From $v = f\lambda$ , a smaller $v$ with unchanged $f$ means a shorter $\lambda$ . The colour we see follows the frequency, so it does not change.

Your turn— tap to reveal the worked answer (9702/11/M/J/25 Q27)

Which of these wavelengths in free space could be green light? (9702/11/M/J/25 Q27)

Answer: a value inside the visible band near the middle, about 500 to 550 nm (5 × 10⁻⁷ m), not 5 μm (infrared) or 50 nm (ultraviolet).

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