The Michelson Interferometer

Figure 1.13: Sketch of a Michelson interferometer.

The American physicist Albert Michelson invented the optical interferometer illustrated in figure 1.13. The incoming beam is split into two beams by the half-silvered mirror. Each sub-beam reflects off of another mirror which returns it to the half-silvered mirror, where the two sub-beams recombine as shown. One of the reflecting mirrors is movable by a sensitive micrometer device, allowing the path length of the corresponding sub-beam, and hence the phase relationship between the two sub-beams, to be altered. As figure 1.13 shows, the difference in path length between the two sub-beams is $2x$ because the horizontal sub-beam traverses the path twice. Thus, constructive interference occurs when this path difference is an integral number of wavelengths, i. e.,

$$2x = m \lambda , ~~ m = 0, \pm 1, \pm 2, \ldots ~~~ \mbox{(Michelson interferometer)}$$ (2.22)

where $\lambda$ is the wavelength of the light and $m$ is an integer. Note that $m$ is the number of wavelengths that fits evenly into the distance $2x$.