Wavelength and Frequency Guide: c = fλ, Visible Light Spectrum & EM Waves
The relationship c = f × λ connects the speed of light, frequency, and wavelength. Explore the full EM spectrum and the visible light rainbow by color, nanometers, and terahertz.
Last updated: 2026-04-28
The Fundamental Relationship: c = f × λ
Every electromagnetic wave obeys the equation:
c = f × λ
where:
- c = speed of light in a vacuum = 299,792,458 m/s (exact)
- f = frequency in hertz (Hz)
- λ (lambda) = wavelength in meters
Rearranging: λ = c ÷ f and f = c ÷ λ. Because c is constant, frequency and wavelength are inversely proportional — higher frequency always means shorter wavelength, and vice versa.
The Electromagnetic Spectrum
The EM spectrum spans over 20 orders of magnitude in frequency. All EM waves travel at c in vacuum and differ only in frequency (and thus wavelength and energy). The table below gives representative ranges for each band.
| Band | Frequency Range | Wavelength Range | Common Uses |
|---|---|---|---|
| Radio waves | 3 Hz – 300 GHz | 1 mm – 100,000 km | Broadcasting, Wi-Fi, radar |
| Microwaves | 300 MHz – 300 GHz | 1 mm – 1 m | Microwave ovens, 5G, satellite |
| Infrared (IR) | 300 GHz – 430 THz | 700 nm – 1 mm | Heat sensing, remote controls |
| Visible light | 430 – 790 THz | 380 – 700 nm | Human vision |
| Ultraviolet (UV) | 790 THz – 30 PHz | 10 – 380 nm | Sterilization, sunburn |
| X-rays | 30 PHz – 30 EHz | 0.01 – 10 nm | Medical imaging, security |
| Gamma rays | >30 EHz | <0.01 nm | Nuclear physics, cancer therapy |
Visible Light Spectrum by Color
Human vision responds to wavelengths between roughly 380 nm and 750 nm. Within this narrow band, wavelength determines perceived color. The table uses consensus values from the CIE and optics literature.
| Color | Wavelength Range (nm) | Frequency Range (THz) | Photon Energy (eV) |
|---|---|---|---|
| Violet | 380 – 450 | 666 – 789 | 2.76 – 3.26 |
| Blue | 450 – 495 | 606 – 666 | 2.51 – 2.76 |
| Cyan | 495 – 520 | 577 – 606 | 2.39 – 2.51 |
| Green | 520 – 565 | 531 – 577 | 2.19 – 2.39 |
| Yellow | 565 – 590 | 508 – 531 | 2.10 – 2.19 |
| Orange | 590 – 625 | 480 – 508 | 1.98 – 2.10 |
| Red | 625 – 750 | 400 – 480 | 1.65 – 1.98 |
Wavelength and Photon Energy
Photon energy is related to frequency by E = h × f, where h = 6.626 × 10−³&sup4; J·s (Planck's constant). Since f = c / λ, energy also equals E = h × c / λ. This means shorter wavelength (higher frequency) photons carry more energy — which is why UV radiation can damage DNA while visible light does not.
Worked Example
What is the wavelength of a 100 MHz FM radio signal?
- f = 100 MHz = 1 × 10&sup8; Hz
- λ = c ÷ f = 299,792,458 ÷ 100,000,000 ≈ 3.00 m
FM radio antennas are typically half a wavelength long (≈ 1.5 m) for optimal reception — a direct application of this formula.
Explore speed unit conversions with our speed converter, or convert energy units related to photon energy with our energy converter.