Michelson interferometer

Maybe you have ever heard that "light+light=darkness". Today, we will try to explain this and build a home-made Michelson interferometer to prove it.

Interferences

In physics, we define an interference as the superposition of two or more waves. Depending on the kind of wave, the pattern is different: for example, the interference of two spherical waves is a pattern of rings, while the pattern for plane waves are fringes.

But, why don't we see this phenomenon if we switch on two lamps?

Well, it has to do with the "coherence": for a simple explanation, we could translate this in waves coming from the same source or having nearly the same frequency. It is also possible to get them with non-monochromatic waves, but in these case they have to have the same range of wavelengths and same phase differences for each wavelenght (for instance, you can see interferences from sunlight when there is oil on a road).

Michelson interferometer

In the picture below, you can see what is called Michelson interferomter.

Let's explain how it works: coherent light emitted from a source (for example, a laser or a sodium lamp) travels up to a beamsplitter (BS), a device capable of dividing a beam into two beams (it is basically a glass with one of its surfaces partially reflective). From there, one of the beams goes to a first mirror (M1) where it is reflected; the same happens to the second beam. In the beamsplitter they meet again and travel together to the observation screen. Notice that there is an adittional glass (the blue one in the figure) to compensate the paths (the first beam goes twice through the beamsplitter and the second one just once).

In the following film from the Celtic Mad Scientist you can learn how to build your own Michelson interferometer, as well as applications and a detailed description of the setup:

For students of advanced levels, you should notice that if the interferometer was perfectly align you would get the interference of two plane waves with the same propagation vector (as they should be pararell) and thus there should not be interference fringes! Obviously, it is not the case here: since it is not perfectly aligned, there is a slighty angle between the two beams that allows you to see the fringes.

As curiosity you should know that, together with Edward Morley, Abraham Michelson tried to demonstrate with this system the existence of the "ether" in 1887. In the 19th century, it was believed that the Earth was surronded by a gas called ether. Michelson and Morley wanted to measure the speed of the Earth with respect to the ether. This movement will produce a wind and, since the light propagated through the ether, the speed of light would be different depending on the propagation direction. In one of the interferometer arms, the light would propagate in the same direction as the wind, but in the other one would propagate against the wind and thus more slowly.

However, they did not find any differences; the "failure" of the experiment showed the non-existance of ether and the propagation of light in vacuum.

In this link, you can find an interactive movie where you can reproduce the experiment and in the AIP Center for History of Physics you can download the original article.