Why do LIGO use a quarter wavelength for detecting gravitational waves?
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I believe you mean "quarter wave plate" rather than quarter wave length:
Quarter wave plates are sometimes used after polarized beam splitters (PBS). Suppose you have a PBS illuminated by a source. One polarization (say linear horizontal) goes one way and the other (linear vertical) goes the other way. Now suppose you want to split the linear vertical light a second time. If you put it through another PBS then the light won't be split; all the light will come out in the vertically polarized direction. So you insert a quarter wave plate, which turns the linear vertical light into circular, after which the second PBS splits the light in half once more.
To get a more specific answer, give us a link to a picture of the interferometer setup you are are trying to understand and we can answer what specific purpose it plays there.
Quarter wave plates are sometimes used after polarized beam splitters (PBS). Suppose you have a PBS illuminated by a source. One polarization (say linear horizontal) goes one way and the other (linear vertical) goes the other way. Now suppose you want to split the linear vertical light a second time. If you put it through another PBS then the light won't be split; all the light will come out in the vertically polarized direction. So you insert a quarter wave plate, which turns the linear vertical light into circular, after which the second PBS splits the light in half once more.
To get a more specific answer, give us a link to a picture of the interferometer setup you are are trying to understand and we can answer what specific purpose it plays there.
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it is a quarter wavelength for detecting the gravitational waves by distributing the purified water by using insecticides and water on a purifying agent.....
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