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An interferometer works on the principle that two waves that coincide with the same phase will amplify each other while two waves that have opposite phases will cancel each other out.

The basic building blocks of this device are a monochromatic light source, usually a laser, a detector, two mirrors and one semitransparent mirror. These are put together as shown in the figure.

                  |    semitransparent
   light          |    mirror
   source         |  /
  ---+            | /         |
     |            |/          |
   *--------------/-----------| mirror
     |           /|           |
  ---+          / |           |
               /  |
                | | | detector

Minuscule changes in the distance between either mirror and the semitransparent mirror will result in large changes in the amount of light energy the detector picks up.

An interferometer allows very precise distance measurements. By moving one mirror slowly away, the detector will show a regular decrease and increase of luminosity. The distance between two peaks in the detector corresponds exactly to one wavelength of the light used.

I think the diagram above is a /Michelson interferometer. (Correct me if i'm wrong, physics happened 20 years ago for me :-) This was the one used in the famous Michelson-Morley experiment that provides evidence for special relativity.

Of course, in Michelson's day, they didn't have lasers, so instead they used a gas discharge lamp, a filter, and a thin slot or pinhole to make more-or-less coherent monochomatic light.

In one version of the Michelson-Morley experiment, they even ran the interferometer off starlight.

Depending on your browser, it might not be obvious that the semitransparent mirror is at 45 degrees to the direction of the light beam. There are two paths from the light source to the detector. One reflects off the semi-transparent mirror, goes to the top mirror and then reflects back, goes through the semi-transparent mirror, to the detector. The other first goes through the semi-transparent mirror, to the mirror on the right, reflects back to the semi-transparent mirror, then reflects from the semi-transparent mirror into the detector.

If these two paths differ by a whole number (including 0) of wavelengths, there is constructive interference and a strong signal at the detector. If they differ by a whole number and a half wavelengths (eg, 0.5, 1.5, 2.5 ...) there is destructive interference and a weak signal.

There are many other types of interferometer. They all work on the same basic principles, but the geometry is different for the different types.

Mention of the use of radio-telescope interferometers would probably also be sensible, as this is probably the most wide spread use of the technique (at least that I know off, although its outside my field so I may be wrong). Of course these devices make no use at all of mirrors! I think there are some light based interferometer telescopes also.