Intro Physics Lab Interferometry Question (Fabry-Perot vs. Michelson)

[Mr. Jones]

Homework Statement

The Michelson interferometer can be used to measure extremely small distance scales. What is the smallest distance scale that can be measured? What uncertainty is associated with this?

What is the smallest scale that can be measured by the Fabry-Perot interferometer? Which is better, the Michelson or the Fabry-Perot?

Homework Equations

λ=(2d_m)/m. This is where λ is the wavelength of the laser being used in conjunction with the interferometer, m is the number of fringes that pass through the viewing area, and d_m is the distance that the movable mirror in the interferometer is moved to get those fringes to pass through.

The Attempt at a Solution

My thoughts were that because both interferometers were set up on the same base with the same micrometer adjustment for the adjustable mirrors and are governed by the same equations, that they would be accurate for equally small distance scales.

 

[jbsteele]

However, the Fabry-Perot interferometer is better at measuring very small distance scales because it uses a thicker beam of light and the results are more easily observed. The smallest distance scale that can be measured by either instrument is dictated by the wavelength of the laser being used.

 

[kerimek]

First of all, it is important to note that both the Michelson and Fabry-Perot interferometers are highly sensitive instruments used to measure small distances. However, the smallest distance scale that can be measured by each of these interferometers may vary depending on various factors such as the wavelength of the laser being used, the quality of the optical components, and the overall experimental setup.

In the Michelson interferometer, the smallest distance scale that can be measured is determined by the number of fringes that can be observed. As mentioned in the given equations, this is dependent on the wavelength of the laser and the distance the movable mirror is moved. The smaller the wavelength and the larger the distance moved, the smaller the distance scale that can be measured. However, there will always be some uncertainty associated with this measurement, as it is impossible to have an infinitely small wavelength or to move the mirror an infinitely large distance. This uncertainty can be minimized by using high-quality components and optimizing the experimental setup.

On the other hand, the Fabry-Perot interferometer uses a different principle to measure small distances. It relies on the phenomenon of resonance, where a narrow beam of light is reflected back and forth between two mirrors, creating an interference pattern. The smallest distance scale that can be measured by this interferometer is determined by the spacing between the two mirrors. The smaller the spacing, the smaller the distance scale that can be measured. However, like the Michelson interferometer, there will always be some uncertainty associated with this measurement.

In terms of which interferometer is better, it really depends on the specific application and the desired level of precision. Both interferometers have their own advantages and limitations. The Michelson interferometer is more versatile and can be used for a wider range of measurements, while the Fabry-Perot interferometer is more sensitive and can achieve higher precision in certain cases. Ultimately, the choice between the two would depend on the specific needs of the experiment.