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.

• Introduction to Light Energy

  • All electromagnetic radiation, or light energy, travels at a particular wavelength and carries a certain amount of energy.
  • Each type of electromagnetic radiation travels at a particular wavelength.
  • The longer the wavelength, the less energy is carried.
  • This radiation exists at different wavelengths, each of which has its own characteristic energy.
  • All electromagnetic radiation, including visible light, is characterized by its wavelength.

• Electromagnetic Spectrum

  • Wavelength is inversely proportional to wave frequency; hence, gamma rays have very short wavelengths that are a fraction of the size of atoms, whereas other wavelengths can be as long as the universe.
  • Wavelengths of electromagnetic radiation, no matter what medium they are traveling through, are usually quoted in terms of the vacuum wavelength, although this is not always explicitly stated.
  • The behavior of electromagnetic radiation depends on its wavelength.
  • Wave number = 1/wavelength in cm Speed of light = wavelength x frequency Energy = Planck's constant x frequency.
  • The wavelengths of various regions of the electromagnetic spectrum are shown alongside an approximate proxy for size of the 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.

• Background

  • Visible wavelengths cover a range from approximately 400 to 800 nm.
  • The longest visible wavelength is red and the shortest is violet.
  • Other common colors of the spectrum, in order of decreasing wavelength, may be remembered by the mnemonic: ROY G BIV.
  • In horizontal diagrams, such as the one on the bottom left, wavelength will increase on moving from left to right.
  • The remaining light will then assume the complementary color to the wavelength(s) absorbed.

• 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.

• The Electromagnetic Spectrum

  • This electromagnetic spectrum ranges from very short wavelengths (including gamma and x-rays) to very long wavelengths (including microwaves and broadcast radio waves).
  • The following chart displays many of the important regions of this spectrum, and demonstrates the inverse relationship between wavelength and frequency (shown in the top equation below the chart).
  • The bottom equation describes this relationship, which provides the energy carried by a photon of a given wavelength of radiation.

• Wavelength, Frequency, and Pitch

  • This is the wavelength, and it affects the pitch of the sound; the closer together the waves are, the higher the tone sounds.
  • So waves with a shorter wavelength arrive (at your ear, for example) more often (frequently) than longer waves.
  • The shorter the wavelength, the higher the frequency, and the higher the pitch, of the sound.
  • Since the sounds are travelling at about the same speed, the one with the shorter wavelength "waves" more frequently; it has a higher frequency, or pitch.

• 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.