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 They are all transverse waves They all travel at the same speed c = 3.00 × 10⁸ m s⁻¹ in a vacuum They can all travel through a vacuum (no medium required) They all transfer energy They can all be reflected, refracted, diffracted, and exhibit interference They can all be polarised They all obey v = fλ (so in vacuum: c = fλ) They are produced by accelerating charges or energy transitions Structure of an EM Wave An electromagnetic wave consists of: An oscillating electric field (E-field) An oscillating magnetic field (B-field) The two fields are perpendicular to each other Both fields are perpendicular to the direction of wave travel The fields oscillate in phase with each other 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) 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): R unny M ashed I nstant V egetables U sually X -tremely G ross (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): Violet: ~400 nm Blue: ~450 nm Green: ~550 nm Yellow: ~580 nm Orange: ~600 nm Red: ~700 nm Memory Aid R ichard O f Y ork G ave B attle I n V ain (Red, Orange, Yellow, Green, Blue, Indigo, Violet-decreasing wavelength) Wave Equation for EM Waves In a vacuum or free space: c = fλ where: c = 3.00 × 10⁸ m s⁻¹ f = frequency (Hz) λ = wavelength (m) Since c is constant, frequency and wavelength are inversely proportional: Higher frequency → shorter wavelength Lower frequency → longer wavelength Concept Insight: EM Wave Production All electromagnetic waves originate from accelerating electric charges or from electron transitions between energy levels: Radio waves: oscillating currents in antennas Microwaves: oscillating currents in cavity magnetrons Infrared: vibrating molecules (thermal emission) Visible light: electron transitions in atoms UV, X-rays, Gamma: high-energy electron transitions, nuclear processes 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 = fraction = fraction = 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 = fraction = fraction = 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 = fraction = fraction = 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 Thinking different EM waves have different speeds in vacuum: All EM waves travel at…
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