# Astronomy 217

## Prof. Andrew W. Steiner

Sep. 24, 2021

TA James Ternullo

• 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).