Measurements with a Michelson Interferometer forrásának megtekintése

Since a light beam can be modelled as oscillating electric and magnetic field, when two or
more beams meet the electric and magnetic fields are added due to the superposition principle. That is
in every point of the space the electric and magnetic field is the vectorial sum of fields of each beam.

If the beams originate from different sources, generally there is no connection between the
electromagnetic oscillations. In every moment there are points is space where adding the fields results
in maximum and points where results in cancellation. Since there is no definite connection, where a
maximum was at a given moment, in the next moment there can be a minimum. The frequency of the
visible light is too high for the human eye, it will average out the fast oscillation of the intensity.

If the beams originate from the same source, there is a correlation between the phase of the
oscillations, so points can exist, where the beams are in phase continously. In this case the total fields
are always maximal in these points, and bright spot is visible there. In the points where the beams are
always in opposite phase, the total intensity is minimal, a dark spot is visible.

First Thomas Young made interference patterns with two closely placed slits. The resulting
image consisted of bright and dark stripes. This experiment was an important proof of the wave nature of
light.

The slits can be used as simple interferometer. If the distance between the slits is known, the
wavelength of the light can be determined by measuring the distance of the maxima and minima. If the
wavelength is known, the distance of the slits can be determined.

==Michelson’s interferometer==
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In 1881, 78 years after Young, A. A. Michelson built a similarily working interferometer.
Michelson’s original intention was to prove the existance of ether – the hypothetical medium which
was considered to be responsible for the propagation of electromagnetic radiation (such as light). Partially his work proves that this hypothesis was wrong. Furthermore, Michelson’s interferometer is widely used to
measure the wavelenght of light, or if it is known, to measure very small displacements. 

On Fig.1 the sketch of Michelson’s interferometer is shown. The beam of laser is split by a
beam splitter, which reflects the 50% of the intensity and transmits the other 50%. One of the split beams
is reflected on a fixed, the other is relfected on a movable mirror. Both beams return to the beam
splitter. Now the half of light reflected from the movable mirror goes to the screen, also the half of the
other beam goes to the screen.

{|  cellpadding="5" cellspacing="5" align="center"
| align="center"|[[Fájl:Michelson_interferometer.jpg|közép|500px]]
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| align="center" style="width: 900px;"|Fig. 1. ''Schematics of the Michelson interferometer''
|}

This way the original beam is split to two different paths and a part of them merge again.
Since the beams originate from the same source, their phase are strongly correlated. If a lens is used
between the laser and the beam splitter, the beams are broadend and an interference pattern consisting
of bright and dark rings is visible on the screen (Fig.2). 

{|  cellpadding="5" cellspacing="5" align="center"
| align="center"|[[Fájl:Hallgatoi laboratorium.jpg|közép|500px]]
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| align="center" style="width: 900px;"|Fig. 2. ''Interference fringes''
|}

Since the two interfering beams of light were split from the same initial beam, they were
initially in phase. Their relative phase, when they meet at any point on the screen, depends on the
difference in the length of their optical paths before reaching that point.

By moving mirror M1, the path length of one of the beams can be varied. Since the beam
traverses the path between M1 and the beam-splitter twice, moving M1 1/4 wavelength nearer the beamsplitter
will reduce the optical path of that beam by 1/2 wavelength. The interference pattern will
change; the radii of the maxima will be reduced so they now occupy the position of the former
minima. If M1 is moved an additional 1/4 wavelength closer to the beam-splitter, the radii of the
maxima will again be reduced so maxima and minima trade positions. However, this new arrangement
will be indistinguishable from the original pattern.

By slowly moving M1 a measured distance $d_N$, and counting $N$, the number of times the fringe
pattern is restored to its original state, the wavelength of the light (λ) can be calculated as: 
$$\lambda=\frac{2d_N}{N}$$
If the wavelength of the light is known, the same procedure can be used to measure $d_N$.

From Fig.1 it is evident, that one of the beams crosses the beam splitter only once, while the
other three-times. If the light source is strongly coherent and monochromatic, such as a laser, it is not a
problem. Although in case of other light sources it can result in error. As the length of optical path
increases, the coherence of split beams is decreasing, which can distort the interference pattern.

Using a compensator plate (see Fig.1) both beams crosses glass object three-times, which
solves this problem. The compensator plate is similar as the beamsplitter, but without reflecting
coating.

With Michelson’s interferometer one can examine optical devices. E.g. placing a lens, as only
one of the split beams crosses it, every small deviation of the lens will result in strong distortion of the
interference pattern. 
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