Michelson Interferometer

In its easiest version, a Michelson interferometer is composed of a light source, of two reflecting plane mirrors, of a half-reflecting blade and of a screen. Figure 9 describes the experimental device. Mirror 1 is located at distance from the blade and mirror 2 at distance . Following both paths, we have two optical systems that play the role of the mirror. For path no 1: splitter then mirror . So source 1, the image of primary source , is given by the symmetric of in relation to the splitter, then by the symmetric in relation to .The gait is equal on path no 2 with mirror , then the splitter blade.

So the device is equal to a Young holes system as it is described on Figure 10.

Mirrors are not necessarily located at the same distance from the blade and the equivalent geometry secondary sources are not necessarily in the same planee or on the same axis. If mirror 2, for example, is switched from an angle in relation to the optical axis, both secondary sources are also shifted. We are going back to the configuration described in the “Interferences: Fundamentals” class, paragraph I.B.6. For any point from the coordinates screen , the interferences phase is:

The fringes observed are the ones described in Figure 6 of the “Interferences: Fundamentals” class.

Michelson interferometer can also be configured to work with plane waves. In this case, there is just to collimate the initial wave with a lens: The source is placed in a lens focus and the mirrors are lit in parallel light thus in plane waves. Figure 11 schematizes the circuitry.

We are in the case treated by paragraph I.B.5 of class “Interferences: Fundamentals”. Inclinations of mirrors 1 and 2 give the waves vectors of both secondary plane waves. Let us consider that mirror 1 is perpendicular with the optical axis and that mirror 2 is switched from an angle following and following . The waves vectors are written:

In the plan , the wave surface slopes are and . In all points f the screen, the interferences phase is given by:

And the interferences signal is written:

The interfringe following is given by:

And the interfringe following is given by:

Figure 12 shows the spatial field of interferences in the superposition area of both waves in function of mirror 2 inclination in both directions and (namely and ).