Michelson Interferometer and mirror

In summary, a Michelson interferometer with a semi-transparent mirror and no absorption has a reflection coefficient for intensity, R, and transmission of T=1-R. The intensities of the light in the two outputs can be calculated as a function of delta_x = x_2-x_1, the difference in arm length. Using general equations for the electric fields of the initial beam, transmitted and reflected electric fields, the reflection and transmission coefficients can be calculated as R=1/4 1/2 and T=1/2 1/2. Applying these coefficients to the two electric fields, we can obtain two equations as a function of delta_x. Further help is needed to determine the exact equation for delta_x.
  • #1
doublemint
141
0
Consider a Michelson interferometer with semi-transparent mirror with a reflection coefficient for the intensity, R and transmission of T=1-R. The mirror does not absorb anything.
Calculate the intensities of the light in the two outputs as a function of delta_x = x_2-x_1 which is the difference in arm length.

I sort had an idea..I calculated the reflection and transmission coefficient based on the electric fields of the initial beam and the transmitted and reflected electric fields. (I used general equations used to derive the total intensity of the light from the interferometer)
It turns out it is R=[STRIKE]1/4[/STRIKE] 1/2 and T=[STRIKE]1/2[/STRIKE] 1/2

I tried applying these coefficients to the two electric fields as they transmit and reflect, but I don't know who to get two equations as a function of delta_x...

If anyone has any hints, I would be very grateful!
Thanks
DM
 
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  • #2
doublemint said:
Consider a Michelson interferometer with semi-transparent mirror with a reflection coefficient for the intensity, R and transmission of T=1-R. The mirror does not absorb anything.
Calculate the intensities of the light in the two outputs as a function of delta_x = x_2-x_1 which is the difference in arm length.

I sort had an idea..I calculated the reflection and transmission coefficient based on the electric fields of the initial beam and the transmitted and reflected electric fields. (I used general equations used to derive the total intensity of the light from the interferometer)
It turns out it is R=[STRIKE]1/4[/STRIKE] 1/2 and T=[STRIKE]1/2[/STRIKE] 1/2

I tried applying these coefficients to the two electric fields as they transmit and reflect, but I don't know who to get two equations as a function of delta_x...

If anyone has any hints, I would be very grateful!
Thanks
DM


Can you give me a hint about your equation for delta_x?
 

What is a Michelson Interferometer?

A Michelson Interferometer is a scientific instrument used to measure the wavelength of light and other optical phenomena. It consists of a beam splitter, two mirrors, and a detector. The beam splitter divides a beam of light into two paths, which are then recombined at the detector. The interference pattern produced by the recombined beams can be used to measure the wavelength of light or detect small changes in the path length of the beams.

How does a Michelson Interferometer work?

The Michelson Interferometer works by splitting a beam of light into two paths using a beam splitter. One path is reflected off a fixed mirror, while the other path is reflected off a movable mirror. The two paths are then recombined at the detector, where an interference pattern is produced. Changes in the path length of one of the beams will cause a shift in the interference pattern, which can be measured and used to calculate the wavelength of light or other optical phenomena.

What is the purpose of using mirrors in a Michelson Interferometer?

The mirrors in a Michelson Interferometer are used to reflect the light beams and recombine them at the detector. The fixed mirror reflects one of the beams, while the movable mirror reflects the other beam. By changing the position of the movable mirror, the path length of one of the beams can be altered, which allows for the measurement of small changes in the interference pattern.

What are some applications of a Michelson Interferometer?

A Michelson Interferometer has many applications in science and technology. It is commonly used in the field of optics to measure the wavelength of light and to study the effects of interference. It is also used in interferometry, which is a technique for measuring small changes in distance. Other applications include testing the flatness of surfaces, measuring the refractive index of materials, and studying the properties of thin films.

Are there any limitations to using a Michelson Interferometer?

While the Michelson Interferometer is a versatile and powerful instrument, it does have some limitations. It is most effective for measuring small changes in path length, so it may not be suitable for measuring large distances. Additionally, it is sensitive to external vibrations and movements, so it must be operated in a stable environment. Finally, it is limited to measuring optical phenomena and cannot be used for other types of measurements.

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