# Light

Key points: wave-particle duality; interference; temperature; inverse r squared law; luminosity; the electromagnetic spectrum

Most of what we know about astronomy has been learned by studying light, so it is important to understand how it behaves. Light is a form of electromagnetic radiation, vibrating electric and magnetic fields moving through space. The Greek letter lambda ( ) is used for the distance between crests, or the "wavelength". (From Nick Strobel Go to his site at www.astronomynotes.com for the updated and corrected version.)

Light is also a form of fundamental particle, called a photon. That is,

Light has "wave-particle duality"

## Wave properties:

1. Diffraction   When light encounters a barrier, such as a slit, its path bends and it can illuminate areas behind the slit that are larger than the width of the slit. Here are water waves at a breakwater; diffraction causes the semi-circular pattern behind the breakwater (to left, from http://www.exploratorium.edu/) and diffraction in action to right.(animation by G. Rieke) 2. Interference How interference works: the black wave is the sum of the blue and green ones. When the blue one is "in phase" with the green, they interfere constructively and the black one is larger than either. When the blue one is "out of phase", they interfere destructively and cancel each other out; the black wave vanishes. (animation by G. Rieke). Rather than drawing the curvy lines for a wave, sometimes we just draw a straight line for the wave crest seen from the top. Here is how the interference animation transfers to this version. (by G. Rieke). Many experiments show that light interferes with itself, a general property of waves. Here is an example with water waves, created at two spots. The picture shows how they add and subtract to create a complex pattern of ripples.This process is interference. To the right, an animation shows how an interference pattern changes with time. from Tom Holub, http://www.flickr.com/photos/physicsclassroom/galleries/72157625109662093/ and Robert Hauenstein, Oklahoma State http://physics.okstate.edu/hauenst/class/ph2414/suppl/waves2/int.html We will show the kind of experiment used to see light interference after the discussion of diffraction and particle behavior.

## Particle properties:

1. Discrete energies

Photons have specific, discrete energies; the shorter their wavelength, the greater the energy (to be discussed below).

2. Isolated arrival times

 Here is a movie of a comet, taken with a device that amplifies low light levels and shows every photon. Note the grainy appearance, due to the detection of individual photons from the sky. This appearance results directly from the discrete energy and isolated arrival times of the photons.from Peter McCullough, http://www.astro.uiuc.edu/~pmcc/comet/pinhole.html Wave-Particle Duality:   An image from a real Young's fringes experiment. (from Andrew Boyd, http://www.uh.edu/engines/two_slits-b.jpg)

If you find this experiment troublesome -- well, so does everyone else However, it is known to be a basic aspect of the behavior not only of photons of light, but of all fundamental particles such as electrons and protons! This topic has become an entire branch of physics called quantum mechanics.

Electromagnetic Spectrum:

 With changing wavelength, short wavelength to long wavelength, we go from: gamma-rays => x-rays => ultraviolet => visible => infrared => microwave =>   radio (A nanometer = nm is 10-9 m) (From Hopkins Ultraviolet Telescope Project, http://praxis.pha.jhu.edu/.) These are all forms of “light” or electromagnetic radiation.

## Some Basic Properties:

The speed of light, c, is a universal constant

c = 3 x 108 meters/sec or c = 3 x 105 kilometers/sec

c = times where is wavelength and is frequency. The frequency is the number of wave crests that pass by a given fixed point per second. From this equation, if we know the wavelength we can compute the frequency, or if we know the frequency we can compute the wavelength.

We call a particle of light a photon, so it travels at speed c, obeys the above relationship between wavelength and frequency and it also follows this relation:

E = h times = h = h times c divided by = hc/ where E is energy, h is a constant called Planck’s constant and is frequency. Thus, if we know the wavelength or frequency, we can compute the energy.

## Temperature measures the energy in motions of atoms.

The "Kelvin" temperature scale sets 0 at the lowest possible temperature, where the atomic motions are "stopped" (to the limits set by quantum mechanics). The speed of motion of molecules is proportional to the square root of  T(Kelvin) divided by the mass of the molecules. We compare hydrogen (yellow, mass = 2) with oxygen (blue, mass = 32) to the left. As the temperature goes up, the speed of the molecules increases (especially for the low mass ones) and they hit the walls of the box harder. Thus, their force on the container walls (the pressure) increases. (animation by G. Rieke)

Examples: 0o Kelvin = -459o F;

273o K = 32o F = 0o C

Note that Centigrade (or Celsius) degrees are the same size as Kelvin degrees.

Fahrenheit degrees are only 5/9ths as large. As objects get hotter, they emit more and at shorter wavelengths. (animation by G. Rieke) The curves as shown to the left are called blackbody curves – they represent the distribution over wavelength of the energy emitted by a hot object whose surface would appear perfectly black if it were cool. Many astronomical objects radiate energy almost as though they were blackbodies.We now discuss the basic "radiation laws" that describe te behavior of blackbody radiators in physical terms: Stefan-Boltzmann Law Wien Displacement Law Inverse r squared behavior The rapid increase of energy with temperature is why we can display only a limited range of temperatures in a "linear" graph like the one above. We can do better with a "logarithmic" graph where the divisions are in factors of ten : where F = number of photons produced by the source and r = object’s distance This equation follows from the area of a sphere centered on the source, . If the brightness fell off with distance slower than , photons would have to be created in empty space to add to those from the source. If it fell off faster, then photons would have to disappear into empty space. (From Clem Pryke,  http://find.uchicago.edu/~pryke/compton/flyer.html)

Light is attracted by gravitational fields.

 According to Einstein's theory of relativity, light is attracted by gravitational fields. This effect was originally confirmed by observing the apparent shift in the positions of stars as their light grazed the limb of the sun, but is now observed in many other situations. Animation from Firstscience.com, http://www.firstscience.com/site/articles/einstein.asp     Rainbow, from  http://www.lioncrusher.com/ecard/ Click to return to syllabus Click to return to Physical Laws hypertext G. H. Rieke Click to go to Spectroscopy