Week 13: Interference and Diffraction 425
Hot sources are thus coherent, but only over acomparatively short time. We use the
heuristic arguments above todefinethe time over which a hot source (or any source) will
remain coherent – thecoherence time: τcoh. For most hot sources in the visible band
of frequencies, the coherence time is on the order of a few tens tohundreds of optical
periods. A reasonable round number might be:τcoh≈ 10 −^12 seconds (1017)(given frequencies in the range of 10^14 to 10^15 cycles per second).
Light, of course, doesn’t travel very far in such a short time. We can define thecoherence
lengthof light as the distance light travels in the coherence time:Lcoh=cτcoh≈ 10 −^4 meters (1018)In all of the text below, we will therefore assume that all of the relevant length scales (such
as the maximum path difference in interference problems) is smaller than 0.1 millimeter,
or 100 microns. For slit separations or film thicknesses much larger than this, interference
will generally be washed out by the random phase shifts associated by hot sources.
Coherent sources in the range of frequences that we might generally call “radio waves”
of all sorts are common as dirt in our society. Every device that transmits energy and
information over a carrier frequency to a remote receiver relies onthe coherence of the
transmitted wave to permit information to be encoded on top of that wave.
Coherent sources in the optical regime are correspondinglyrareand for all practical
purposes there is just one source of coherent optical radiation –the laser. The laser
is nearly unique as a source of monochromatic coherent light. Lasers typically have
coherence lengths measured inmeters. Lasers are so coherent that light from twodifferent
lasers produces a stable interference pattern. Laser light can besplit and sent along two
very different path lengths and still interfere. This is the basis of laser holography^114 ,
the ring laser gyroscope^115 and laser interferometry^116.
All other sources of visible light generally rely onatomsto produce the actual light, most
often atoms that arehot, hot enough to glow as they thermally bounce off of each other
at high speed, exciting various electric “oscillators” in their quantumstructure. The sun
is a very hot source (surface temperature around 5778◦K). Incandescent bulbs produce
light from a hot tungsten filament that is joule heated to some 3600◦K. Fluorescent
bulbs operate much cooler – the optimum bulb temperature is around 313 ◦K (40◦C or
104 ◦F) but are still “hot” in the sense of thermally random and chaotic.
Finally, one of the most recent developments in electrical lighting is the increasing preva-
lence of light emitting diodes (LEDs) as commercially important sources of light. LEDs
actually operate at room temperatures and are so efficient that their temperature gener-
ally doesn’t greatly exceed the ambient temperature – nearly all of the energy delivered
to them emerges as light. LEDs are usually more or less monochromatic, emitting light
at particular wavelengths determined by the quantum properties of the semiconductors
that make up the diode. In this they arealmostidentical to solid state diode-based
lasers, except in the one important regard – they are still “hot” incoherent sources.
Pay careful attention to coherence as you work through interference and diffraction below.
Remember, even hot (monochromatic) sources will usually produceinterference when the
light being summed is within the mutual coherence time/length of the light source in(^114) Wikipedia: http://www.wikipedia.org/wiki/Holography.This is actually a fascinating topic and a great thing for
someone seeking an extra credit project to try out. It does, however, require a laser, film and a darkroom, and a very,
very solid/motionless lab bench to use as a base, and probably won’t work the first time you try it.
(^115) Wikipedia: http://www.wikipedia.org/wiki/ring laser gyroscope.
(^116) Wikipedia: http://www.wikipedia.org/wiki/interferometry.