Astronomy 217

 
 

Prof. Andrew W. Steiner

 
 
Sep. 24, 2021
 
 

TA James Ternullo

Last Time

  • Eclipses

Today

  • Wave Theory of Light
  • Photoelectric Effect
  • Kirchoff's Laws

Wave Theory

  • René Descartes (1596–1650) in 1637 published a theory for the refraction of light based on light traveling as a wave.
  • Though he incorrectly assumed that light, like sound, travels faster in a denser medium, this is nonetheless seen as the beginnings of the wave theory of light.
  • The principle descriptor of a traveling wave is the wavelength, λ, the distance between successive crests or troughs.
  • This can be related to the frequency, \( \nu \), of crest/trough passage and the speed of light, c, by \( \lambda = c/ {\nu} \)
 

Speed of light

  • Directly measuring the speed of light with the quality of timekeeping available in the 17th century required very long distances.
  • In 1676, Danish astronomer Olaus Römer noticed that the observed time for eclipses of Io by Jupiter differed from predictions using Kepler’s Law in a predictable way.
  • When Earth was further away from Jupiter, the eclipses were delayed as much as 22 minutes.
  • Römer and his colleagues ascribed the difference to the finite speed of light. Crossing 2 AU in 22 minutes requires a velocity \( c = 2.27 \times 10^{8}~\mathrm{m}/\mathrm{s} \)
 

Huygen's Principle

  • Huygens formulated a wave theory with much greater explanatory power than previous attempts. Central to the power of Huygen’s theory is the principle
  • The wavefront of a propagating wave of light at any instant conforms to the envelope of spherical wavelets emanating from every point on the wavefront at the prior instant.
  • Huygen’s principle is critical to understanding the interactions of waves and obstructions.
 

Prisms

  • One of the observations that was difficult to resolve with the wave theory was the appearance of spectrum of colors when white light passed through a prism.
  • The common belief was that the colors were a contamination caused by the prism.

Young's Experiment

  • The most influential of the experiments supporting the wave theory was Thomas Young’s 1801 double slit experiment.
  • The interference of the coherent light passing through the two slits produces a pattern of dark and light bands where the interference is destructive or constructive.
  • Young was also the first to measure the wavelength of light.

Doppler Shift

  • In 1842, Christian Doppler proposed another consequence of the wave theory of light:
  • The wavelength of light from an approaching light source is shortened.
  • $$ \lambda^{\prime} = \lambda (1+\frac{v}{c}) $$

Electrostatic Field

  • Before we discuss electromagnetism, we must start with the electric field.
  • Charles Augustin de Coulomb (1736-1806) published in 1785 what we now term Coulomb’s Law. $$ F_e = \frac{K_e q_1 q_2}{r^2} $$
  • Michael Faraday (1791-1867) first expresses this in terms of an electric field originating from any charge, $$ \vec{E} = \frac{K_e q}{r^2} \hat{r} = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r^2} \hat{r} $$

Electromagnetism

  • On 21 April 1820, Hans Christian Ørsted (1777-1851) observed that current passing along a wire deflected a nearby compass needle, thus relating electricity and magnetism.
  • Work by Faraday and James Clerk Maxwell (1831-1879) produced the unified theory of electromagnetism, embodied in Maxwell’s Equations.
  • Maxwell used these equations to show vibrating charges would produce electro-magnetic waves which would travel at the speed of light \( c = ( \mu_0 \varepsilon_0 )^{-1/2} \)
  • Heinrich Hertz (1857-1894) confirmed this result, detecting radio waves in 1886.

Polarization

  • The polarization, or orientation of the electric field in a wave of light, can be a very important characteristic of the light wave as not all physical processes affect all polarizations in the same fashion.
  • In 1845, Faraday observed that the polarization of a light wave rotated as it traveled through a dielectric along a magnetic field.
  • Reflected light is linearly polarized with its electric field vector parallel to the plane of the reflecting surface.

Photoelectric Effect

  • In 1887, Hertz had also observed charged objects lost their charge when exposed to UV, but not visible, light.
  • Later experiments showed the energy of the emitted electrons depended on the frequency.
  • In 1901, Max Planck (1858-1947) had published a successful theory for blackbody radiation based on oscillators whose energies are fixed at \( E = h \nu \) where \( h = 6.626 \times 10^{−34}~\mathrm{J}~\mathrm{s} \).
  • Albert Einstein (1879-1955) in 1905, explained the effect with discrete packets of light, photons, with \( E = h \nu \)

Compton Scattering

  • Additional support for the particle nature of light came from experiments by Arthur Compton (1892-1962) in 1923 that showed that light scattered by electrons changed in wavelength.
  • While wave theory predicted that the wavelength of light would be unaffected by the change in direction, the observations revealed $$ \Delta \lambda = \lambda^{\prime}-\lambda = \frac{h}{m_e c} (1-\cos \theta) $$
  • This is consistent with the energy exchange that occurs when a relativistic particle collides with a stationary target, supporting the particle theory of light.

Modern Colors

  • We now detect electromagnetic waves across 20 orders of magnitude in wavelength.
  • Each type of photon brings different information.
  • Only radio and optical penetrate the atmosphere.

Spectral Lines

  • By the mid-nineteenth century, it was possible to create chemically pure samples of many elements, largely by electrolysis.
  • When light from these elements, made for example by placing a sample in a flame (flame spectroscopy), was passed through a prism, bright emission lines appear on a dark background.

Distinctive Lines

  • Later studies showed that each element had a distinctive set of lines.
  • Using flame spectroscopy to analyze mineral water, Bunsen and Kirchoff discovered Cesium in 1860 and Rubidium in 1861.
  • Compounds reveal the lines of their component atoms, for example, Alter showed in 1854 that the emission lines from brass were those of copper and zinc.

Bright and Dark Lines

  • In contrast to the emission lines from a hot gas, if white light is passed through a cool gas, dark absorption lines appear on a rainbow background.
  • The wavelengths of these lines correspond to those of the emission lines.

Kirchoff's Laws

  • To codify the observed behavior of spectral lines, Kirchhoff, in 1860, presented Three Laws of Spectroscopy.
  • A hot solid or a hot, dense gas produces a continuous spectrum.
  • A hot, low-density gas produces an emission- line spectrum.
  • A continuous spectrum source viewed through a cool, low-density gas produces an absorption- line spectrum.

The Solar Spectrum

  • By 1814, Joseph Frauehofer (1787-1826) cataloged 574 lines in the solar spectrum.
  • In 1861, Kirchoff demonstrated that zinc, gold, cadmium, iron, barium, calcium, lead, silicon, copper and magnesium were present in the Sun. In 1862, Ångström proved the Sun’s atmosphere contained hydrogen.
  • Spectroscopic observations like these led to the discovery of Helium in 1868 by Norman Lockyer (1836-1920) and Pierre Jules Janssen (1824-1907).