# Interferometer to measure refractive index of a gas

• Robsta
In summary, the conversation discusses a two beam interferometer used to monitor changes in refractive index in a gas cell. It is illuminated with monochromatic light and uses polarizing beam splitters to pass and reflect polarized light. The solution to producing equal intensity beams in the interferometer arms is to configure retarder 1 with its ordinary and extraordinary axes at 45 degrees to the incoming polarized light. For optimal modulated interference patterns, polaroid 1 should pass an orientation of polarization and polarizer 2 should be at 45 degrees to combine the vertical and phase shifted horizontal light. Detector 2 also needs a retarder to produce an interference pattern, and the phase shift is caused by the gas slowing down one beam
Robsta

## Homework Statement

I've uploaded a diagram showing a two beam interferometer that can be used to monitor changes of refractive index in a gas cell. it is illuminated with monochromatic light of wavelength λ. The light is linearly horizontally polarised. The two polarizing beam splitters (PBS) pass vertical polarisation and reflect horizontal polarisation.

a) How should retarder 1 be configured to produce beams of equal intensity in the two interferometer arms?

b) Determine the orientation of polarisation which polaroid 1 should pass so that detector 1 can observe an optimally modulated interference pattern

c) Detector 2 should also observe an optimally modulated interference pattern. Determine the configuration of retarder 2 and polariser 2 that will produce an optimally modulated interference signal in which the phase difference of light from the two arms is changed from the phase difference observed on detector 1 by dφ

## The Attempt at a Solution

a) I think retarder one wants to have its ordinary and extraordinary axes at 45 degrees to in incoming polarised light. This will split the light into two components, both polarised at 90 degrees to each other, of equal intensity.

These however won't be vertically and horizontally polarized, they'll be at 45 degrees to that.

b) I don't really see why the system needs two detectors. I see that the light going through the gas will acquire a phase shift due to the different refractive index of the gas. This will make circularly (or elliptically) polarised light at the detector. A polariser will just turn that into linearly polarised light. Will it produce an interference pattern?

I guess for a combination of the vertical light and the phase shifted horizontal light, the polariser should be at 45 degrees so as to combine the two.

c) I don't really see why detector two needs a retarder. Come to that, I dont' really see how the phase shift leads to an interference pattern at all rather than just circularly polarised light.

I'd appreciate any insight into this.

#### Attachments

• interference.jpg
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Look at the Application Examples at the bottom http://www.edmundoptics.com/technical-resources-center/optics/understanding-waveplates/
Also interference is produced by a path difference, in this case by the gas slowing the one beam down
and thus causing a phase difference between the two beams, which in effect is the same as a path difference.
How a laser interferometer works:
http://spie.org/x34353.xml

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## 1. How does an interferometer measure the refractive index of a gas?

An interferometer measures the refractive index of a gas by using the principle of interference. A beam of light is split into two paths, with one path passing through the gas sample and the other path serving as a reference. The two beams are then recombined and the resulting interference pattern is analyzed to determine the refractive index of the gas sample.

## 2. What is the accuracy of an interferometer in measuring the refractive index of a gas?

The accuracy of an interferometer in measuring the refractive index of a gas depends on various factors such as the quality of the instrument, the stability of the light source, and the properties of the gas sample. Typically, interferometers can achieve an accuracy of up to 0.00001 in measuring refractive index.

## 3. Can an interferometer measure the refractive index of any type of gas?

Yes, an interferometer can measure the refractive index of any type of gas as long as the gas is transparent to the wavelength of light used in the measurement. However, the accuracy of the measurement may vary depending on the properties of the gas sample.

## 4. How does the temperature and pressure of the gas affect the refractive index measurement with an interferometer?

The temperature and pressure of the gas can affect the refractive index measurement with an interferometer by changing the density and refractive index of the gas sample. It is important to control and monitor these parameters during the measurement to ensure accurate results.

## 5. What are the limitations of using an interferometer to measure the refractive index of a gas?

One limitation of using an interferometer to measure the refractive index of a gas is that it requires a transparent gas sample. Opaque or highly absorbing gases may not produce a measurable interference pattern. Additionally, interferometers may be sensitive to external factors such as vibrations or air currents, which can affect the accuracy of the measurement.

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