Electromagnetic Spectrum Physics Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
The human eye detects light from 380 nm380 \text{ nm} (violet) to 700 nm700 \text{ nm} (red). What is the range of frequencies for visible light? What fraction of the full EM spectrum (from 3 Hz3 \text{ Hz} radio to 3×1020 Hz3 \times 10^{20} \text{ Hz} gamma) does visible light occupy? Use c=3×108 m/sc = 3 \times 10^8 \text{ m/s}.

Solution

  1. 1
    Violet: f=3×108380×10−9=7.89×1014 Hzf = \frac{3 \times 10^8}{380 \times 10^{-9}} = 7.89 \times 10^{14} \text{ Hz}. Red: f=3×108700×10−9=4.29×1014 Hzf = \frac{3 \times 10^8}{700 \times 10^{-9}} = 4.29 \times 10^{14} \text{ Hz}.
  2. 2
    Visible range spans about 3.6×1014 Hz3.6 \times 10^{14} \text{ Hz}, which is less than one octave of frequency.
  3. 3
    The full EM spectrum spans about 102010^{20} orders of magnitude. Visible light is a tiny sliver: 3.6×10143×1020≈10−6\frac{3.6 \times 10^{14}}{3 \times 10^{20}} \approx 10^{-6}, or about one millionth of the full spectrum.

Answer

fvisible≈4.3×1014 to 7.9×1014 Hz (a tiny fraction of the full spectrum)f_{\text{visible}} \approx 4.3 \times 10^{14} \text{ to } 7.9 \times 10^{14} \text{ Hz (a tiny fraction of the full spectrum)}
Visible light occupies an extremely narrow band of the full electromagnetic spectrum. Most of the universe's EM radiation is invisible to the human eye, which is why we need instruments to detect radio, infrared, UV, and X-ray emissions.

About Electromagnetic Spectrum

The complete continuum of all electromagnetic waves, organized in order of increasing frequency (or decreasing wavelength).

Learn more about Electromagnetic Spectrum →

More Electromagnetic Spectrum Examples

Example 1 easy

Arrange the following EM waves from lowest to highest frequency: visible light, X-rays, radio waves,

Example 2 medium

A photon of ultraviolet light has a wavelength of [formula]. What is its energy? Use [formula] and [

Example 3 medium

A cell phone operates at [formula] and an X-ray machine at [formula]. By what factor is the X-ray fr

← All Electromagnetic Spectrum Examples Electromagnetic Spectrum Concept