27.4

The Michelson Interferometer

An interferometer is an apparatus that can be used to measure the wavelength of light by utilizing interference between two light waves. One particularly famous interferometer is that developed by Albert A. Michelson (1852–1931). The Michelson interferometer uses reflection to set up conditions where two light waves interfere. Figure 27-15 presents a schematic drawing of the instrument. Waves emitted by the monochromatic light source strike a beam splitter, so called because it splits the beam of light into two parts. The beam splitter is a glass plate, the far side of which is coated with a thin layer of silver that reflects part of the beam upward as wave A in the drawing. The coating is so thin, however, that it also allows the remainder of the beam to pass directly through as wave F. Wave A strikes an adjustable mirror and reflects back on itself. It again crosses the beam splitter and then enters the viewing telescope. Wave F strikes a fixed mirror and returns, to be partly reflected into the viewing telescope by the beam splitter. Note that wave A passes through the glass plate of the beam splitter three times in reaching the viewing scope, while wave F passes through it only once. The compensating plate in the path of wave F has the same thickness as the beam splitter plate and ensures that wave F also passes three times through the same thickness of glass on the way to the viewing scope. Thus, an observer who views the superposition of waves A and F through the telescope sees constructive or destructive interference, depending only on the difference in path lengths and traveled by the two waves.

Figure 27-15 A schematic drawing of a Michelson interferometer.

The physics of the Michelson interferometer.

Now suppose the mirrors are perpendicular to each other, the beam splitter makes a 45° angle with each, and the distances and are equal. Waves A and F travel the same distance, and the field of view in the telescope is uniformly bright due to constructive interference. However, if the adjustable mirror is moved away from the telescope by a distance of , wave A travels back and forth by an amount that is twice this value, leading to an extra distance of . Then, the waves are out of phase when they reach the viewing scope, destructive inteference occurs, and the viewer sees a dark field. If the adjustable mirror is moved farther, full brightness returns as soon as the waves are in phase and interfere constructively. The in-phase condition occurs when wave A travels a total extra distance of relative to wave F. Thus, as the mirror is continuously moved, the viewer sees the field of view change from bright to dark, then back to bright, and so on. The amount by which has been changed can be measured and related to the wavelength of the light, since a bright field changes into a dark field and back again each time is changed by a half wavelength. (The back-and-forth change in distance is .) If a sufficiently large number of wavelengths are counted in this manner, the Michelson interferometer can be used to obtain a very accurate value for the wavelength from the measured changes in .

Test your understanding of the material in Sections 27.1, 27.2, 27.3 and 27.4:

· | The Principle of Linear Superposition
· | Young’s Double-Slit Experiment
· | Thin-Film Interference
· | The Michelson Interferometer

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