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 (lambda.jpg (8443 bytes)) is used for the distance between crests, or the "wavelength".

Light as oscillating electric and magnetic fields

(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) animation of diffraction at a slit

2. Interference

Animation showing 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).
Representation of wave tops as lines Rather than drawing the curvy lines for a wave, sometimes we just draw a straight line for the wave crest seen from the top.
Interference in the wave-tops-as-lines view  

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

pinhole.gif (1902129 bytes)

Wave-Particle Duality:

If we shine photons one at a time into the box below, we will detect them as discrete particles, each one at a specific position against the back surface. However, if we collect a large number of photons, even one at a time, they will distribute themselves in the "dark" areas and avoid the "light" ones. The "dark" areas are where the positive wavefronts overlap from the two slits letting each photon through. Thus, they result from the combination of diffraction and interference. Perhaps the most curious part is that each photon must pass through both slits! (since we get the pattern even they go through the slits one at a time). This experiment is called "Young's fringes" after the first scientist to do it. Experiment for yourself at http://www.animatedscience.co.uk/blog/wp-content/uploads/focus_waves/rippletank__ripple.html

Cartoon of box with double slits Animation of interference through double slits

 

 

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 elsebuttonbook.jpg (10323 bytes) 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/.)

emspec.gif (68057 bytes)

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 = lambda.jpg (8443 bytes) times nu.jpg (6708 bytes)

where lambda.jpg (8443 bytes) is wavelength and nu.jpg (6708 bytes) 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 nu.jpg (6708 bytes) = hnu.jpg (6708 bytes) = h times c divided by lambda.jpg (8443 bytes) = hc/lambda.jpg (8443 bytes)

where E is energy, h is a constant called Planck’s constant and nu.jpg (6708 bytes) is frequency. Thus, if we know the wavelength or frequency, we can compute the energy.

Light properties are related to the temperature of the object emitting the light

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.

Animation showing effect of heat on molecular motion 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.

Animation of blackbody output vs. temperature 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
luminosity.jpg (9320 bytes) Stefan-Boltzmann Law: the total energy emitted by a blackbody E = sigma.jpg (7580 bytes)AT4 where E is the energy emitted by an object of area A with temperature T. sigma.jpg (7580 bytes) is a constant. For astronomical sources, we often call the total energy output the "luminosity." The object to the left might have a luminosity of 100 watts, while the sun has one of 3.9x1026 watts. From Clem Pryke, http://find.uchicago.edu/~pryke/compton/flyer.html
Comparison of linear and logarithmic graphs 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 buttonbook.jpg (10323 bytes):
Animation of blackbody behavior vs. temperature  

We plot the blackbody logarithmically and let its temperature rise from 500K to 7600K: (animation by G. Rieke)

The curve has the same shape regardless of temperature, and its peak gets shorter in wavelength as 1/T

Wien Displacement Law: lampeak.jpg (18065 bytes) = 2,900,000/T

where lampeak.jpg (18065 bytes) is the wavelength at which the object's output is a maximum and T is its temperature (in K).

The brightness of a light source (again, it doesn’t matter whether we’re discussing visible light or some other type of electromagnetic radiation) is inversely proportional to the square of the source’s distance from us:

inversersquare.jpg (26597 bytes)

where F = number of photons produced by the source and r = object’s distance

inversersq.jpg (172132 bytes) This equation follows from the area of a sphere centered on the source, spharea.jpg (4693 bytes). If the brightness fell off with distance slower than spharea.jpg (4693 bytes), 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.ribbon.jpg (3557 bytes) Animation from Firstscience.com, http://www.firstscience.com/site/articles/einstein.asp lec24_07.gif (1581 bytes) bend_med.gif (96711 bytes)

What are the key aspects of electromagnetic radiationlink to a key question

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rainbow.jpg (6687 bytes)

 

 

 

 

 

Rainbow, from  http://www.lioncrusher.com/ecard/

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hypertext copyright.jpg (1684 bytes) G. H. Rieke

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