wavelength

Examples of wavelength in the following topics:

• Dispersion: Rainbows and Prisims

  • Dispersion is defined as the spreading of white light into its full spectrum of wavelengths.
  • These colors are associated with different wavelengths of light.
  • Sunlight, considered to be white, actually appears to be a bit yellow because of its mixture of wavelengths, but it does contain all visible wavelengths.
  • But for a given medium, n also depends on wavelength.
  • Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength.

• Visible Light

  • Electromagnetic radiation in this range of wavelengths is often simply referred to as "light".
  • A typical human eye will respond to wavelengths from about 390 to 750 nm (0.39 to 0.75 µm).
  • Red light has the lowest frequencies and longest wavelengths, while violet has the highest frequencies and shortest wavelengths.
  • The range of frequencies and wavelengths is remarkable.
  • Most UV wavelengths are absorbed by oxygen and ozone in Earth's atmosphere.

• Energy and Momentum

  • Electromagnetic waves have energy and momentum that are both associated with their wavelength and frequency.
  • The ratio of speed of light (c) to wavelength (λ) can be substituted in place of f to give the same equation to energy in different terms .
  • Note that energy cannot take any value: it can only exist in increments of frequency times Planck's constant (or Planck's constant times c divided by wavelength).
  • Substituting E with hc/λ cancels the c terms, making momentum also equal to the simple ratio of Planck's constant to wavelength.
  • Relate energy of an electromagnetic wave with the frequency and wavelength

• Dispersion of the Visible Spectrum

  • Visible light is the range of wavelengths of electromagnetic radiation that humans can see.
  • Dispersion is the spreading of white light into its full spectrum of wavelengths.
  • In water, the refractive index varies with wavelength, so the light is dispersed.
  • (a) A pure wavelength of light falls onto a prism and is refracted at both surfaces.
  • Since the index of refraction varies with wavelength, the angles of refraction vary with wavelength.

• Scattering of Light by the Atmosphere

  • From the formula, we can see that a shorter wavelength will be scattered more strongly than a longer one.( The longer the wavelength, the larger the denominator, and from algebra we know that a larger denominator in a fraction means a smaller number. )
  • As we just learned, light scattering is inversely proportional to the fourth power of the light wavelength.
  • So, the shorter the wavelength, the more it will get scattered.
  • Since the light is being scattered less and less, you see the longer wavelengths, like red and yellow.
  • The remaining unscattered light is of longer wavelengths and so appears orange.

• Wavelength, Freqency in Relation to Speed

  • Waves are defined by its frequency, wavelength, and amplitude among others.
  • The wavelength is inversely proportional to the frequency, so an electromagnetic wave with a higher frequency has a shorter wavelength, and vice-versa.
  • We also observe the wavelength, which is the spatial period of the wave (e.g. from crest to crest or trough to trough).
  • We denote the wavelength by the Greek letter $\lambda$.
  • Frequency and wavelength can also be related-* with respects to a "speed" of a wave.

• Microwaves

  • The prefix "micro-" in "microwave" is not meant to suggest a wavelength in the micrometer range.
  • A clear line of sight between transmitter and receiver is needed because of the short wavelengths involved.
  • Sophisticated radar systems can map the Earth and other planets, with a resolution limited by wavelength.
  • The shorter the wavelength of any probe, the smaller the detail it is possible to observe.
  • The range of frequencies and wavelengths is remarkable.

• Infrared Waves

  • Infrared (IR) light is EM radiation with wavelengths longer than those of visible light from 0.74 µm to 1 mm (300 GHz to 1 THz).
  • The wavelength range from approximately 200 μm up to a few mm is often referred to as "sub-millimeter" in astronomy, reserving far infrared for wavelengths below 200 μm.
  • Many astronomical objects emit detectable amounts of IR radiation at non-thermal wavelengths.
  • Most UV wavelengths are absorbed by oxygen and ozone in Earth's atmosphere.
  • The range of frequencies and wavelengths is remarkable.

• X-Rays and the Compton Effect

  • It was observed that when X-rays of a known wavelength interact with atoms, the X-rays are scattered through an angle $\theta$ and emerge at a different wavelength related to $\theta$.
  • Although classical electromagnetism predicted that the wavelength of scattered rays should be equal to the initial wavelength, multiple experiments had found that the wavelength of the scattered rays was longer (corresponding to lower energy) than the initial wavelength.
  • where λ\lambda is the initial wavelength, λ′\lambda' is the wavelength after scattering, $h$ is the Planck constant, mem_e is the Electron rest mass, $c$ is the speed of light, and θ\theta is the scattering angle.
  • The wavelength shift $\lambda ' - \lambda$ is at least zero (for $\theta = 0$°) and at most twice the Compton wavelength of the electron (for $\theta = 180$°).
  • A photon of wavelength $\lambda$ comes in from the left, collides with a target at rest, and a new photon of wavelength $\lambda '$ emerges at an angle $\theta$.

• X-Rays

  • X-rays are electromagnetic waves with wavelengths in the range of 0.01 to 10 nanometers and energies in the range of 100 eV to 100 keV.
  • They are shorter in wavelength than UV rays and longer than gamma rays.
  • The most frequent method of distinguishing between X- and gamma radiation is the basis of wavelength, with radiation shorter than some arbitrary wavelength, such as 10−11 m, defined as gamma rays.
  • X-rays are part of the electromagnetic spectrum, with wavelengths shorter than those of visible light.
  • The range of frequencies and wavelengths is remarkable.