# Amplitudes in a Michelson interferometer

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In summary, the conversation discusses a discrepancy in the result of a Michelson interferometer. It is discovered that the assumption that the resulting waves after hitting the wave splitter have half the amplitude of the original wave does not give the correct irradiance for fringes. Instead, the correct expression is given by assuming that the amplitude of both beams after the beam splitter is still the same as the source amplitude. This raises questions about energy creation in the system.
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Hello,

I am having a hard time understanding a result relating to a michelson interferometer. I always assumed that when the beam hits the wave splitter both resulting waves will have half the amplitude of the original wave. However using this assumption does not give the correct irradiance for fringes on a michelson interferometer. $$I = 4 I_0 * cos^2(\frac {2{\pi}d} {\lambda} + \frac {\pi} {2})$$ Here ##d## is the difference in length between the two arms of the interferometer. I can only arrive at this expression by assuming that the amplitude of both beams after the beam amplitude is still the same as the source amplitude. Is this true, and if so, why is this? Wouldn't you be creating energy in this way?

Thanks!

##I_0## is the intensity of each of the beams after passing the entire system, not the source intensity.

## 1. What is a Michelson interferometer?

A Michelson interferometer is a scientific instrument used to measure small changes in the position of objects, the wavelength of light, and other properties of light. It consists of a beam splitter, two mirrors, and a detector. The beam splitter divides a single beam of light into two beams, which travel along different paths and then recombine to produce an interference pattern on the detector.

## 2. What is the purpose of an interferometer?

The purpose of an interferometer is to measure small changes in the position of objects or properties of light. It can also be used to measure the wavelength of light, which is useful for determining the chemical composition of a substance or the distance to a distant object.

## 3. How do amplitudes in a Michelson interferometer affect measurements?

Amplitudes in a Michelson interferometer can affect measurements by changing the intensity of the interference pattern on the detector. The amplitude of the light waves affects the brightness of the fringes, which can be used to make precise measurements. Any changes in the amplitudes of the light waves can alter the accuracy of the measurements.

## 4. How is the amplitude of the interference pattern affected by the beamsplitter?

The beamsplitter in a Michelson interferometer divides the incoming beam of light into two beams of equal intensity. This means that the amplitude of each beam is half of the original beam's amplitude. When the beams are recombined, the intensity of the interference pattern will depend on the relative phases of the two beams.

## 5. Can the amplitudes in a Michelson interferometer be adjusted?

Yes, the amplitudes in a Michelson interferometer can be adjusted by changing the distance between the mirrors or by changing the wavelength of the light source. By adjusting these parameters, the relative phases of the two beams can be changed, which will affect the intensity of the interference pattern on the detector.

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