How wavelength will be calculated? when movable mirror of micholson inferometer is moved a distance x meters and m fringes pass through a reference point
Answers
Explanation:
Aim:
To determine the wavelength of a laser using the Michelson interferometer
Apparatus:
Laser light source, Michelson interferometer kit, optical bench, meter scale.
Theory:
Interferometers are used to precisely measure the wavelength of optical beams through the creation of interference patterns . The Michelson interferometer is a historically important device which provides simple interferometric configuration, useful for introducing basic principles
Interference theory:
Light is a transverse wave. When two waves of same wavelength and amplitude travel through same medium, their amplitudes combine. A wave of greater or lesser amplitude than the original will be the result. The addition of amplitudes due to superposition of two waves is called interference. If the crest of one wave meets with the trough of the other, the resultant intensity will be zero and the waves are said to interfere destructively. Alternatively, if the crest of one wave meets with the crest of the other, the resultant will be maximum intensity and the waves are said to interfere constructively.
Suppose two coherent (i.e. their initial phase relationship remains constant) waves start from the same point and travel different paths before coming back together and interfering with each other. Suppose also that the re-combined waves illuminate a screen where the position on the screen depends on the difference in the lengths of the paths traveled by the two waves. Then the resulting alternating bright and dark bands on the screen are called interference fringes.
In constructive interference, a bright fringe (band) is obtained on the screen. For constructive interference to occur, the path difference between two beams must be an integral multiple mλ of the wavelength λ, where m is the order, with m =0,1,2...
Michelson Interferometer:
The Michelson interferometer is the best example of what is called an amplitude-splitting interferometer. It was invented in1893 by Albert Michelson, to measure a standard meter in units of the wavelength of the red line of the cadmium spectrum. With an optical interferometer, one can measure distances directly in terms of wavelength of light used, by counting the interference fringes that move when one or the other of two mirrors are moved. In the Michelson interferometer, coherent beams are obtained by splitting a beam of light that originates from a single source with a partially reflecting mirror called a beam splitter. The resulting reflected and transmitted waves are then re-directed by ordinary mirrors to a screen where they superimpose to create fringes. This is known as interference by division of amplitude. This interferometer, used in 1817 in the famous Michelson- Morley experiment, demonstrated the non-existence of an electromagnetic-wave-carrying ether, thus paving the way for the Special theory of Relativity.
Light from a monochromatic source S is divided by a beam splitter (BS), which is oriented at an angle 45° to the beam, producing two beams of equal intensity. The transmitted beam (T) travels to mirror M1 and it is reflected back to BS. 50% of the returning beam is then reflected by the beam splitter and strikes the screen, E. The reflected beam (R) travels to mirror M2, where it is reflected. 50% of this beam passes straight through beam splitter and reaches the screen.
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