Two Beam Splitters example essay topic

Abstract: The interferometer is the most accurate measuring device known to man. It was created by Albert A. Michelson. The operation of the interferometer described briefly is a light beam that is separated by a beam splitter. The two beams then travel equal distances at 90^0 of each other where they are reflected off two mirrors back through the beam splitter. They are then superimposed on to a screen. The screen will display an interference pattern of fringes.

The interferometer is extremely sensitive to vibrations and should be isolated from them The interferometer is the most accurate device presently known to man, and most likely will remain the most accurate measuring device for the next hundred years" Cal Christiansen. The interferometer can measure lengths of one half the wavelength of the light source being used. With a He Ne laser (Helium Neon) this length is 316.4 nm, about 1/3 of a micron. The interferometer is able to measure very small distances by the interference produced between two lasers beams. With this degree of accuracy there are clearly many uses for this device including, measuring flatness, structural stress, and making linear measurements.

Albert A. Michelson is the father of the interferometer and the "Michelson Interferometer" is still used today. Michelson was born in Prussia in 1872 and later moved to the United States where he joined the U.S. Navy. As an instructor in the Navy academy he was asked to demonstrate the Foucault method of measuring the speed of light and made several improvements on it. Michelson received a grant and built his first interferometer much like the one presently used. It consisted of an Arg and lamp, two mirrors, two beam splitters and an eyepiece. The device was extremely sensitive to vibrations and wasn't accurate until it was brought to the Potsdam Astrophysical Observatory in Berlin where it was mounted on a platform designed for an equatorial telescope.

With proper setup Michelson attempted to detect the presence ether, an invisible undetectable material that surrounded by all matter. This was unsuccessful and Einstein later declared that the ether did not exit and light travels at the same speed in all directions. Michelson would later receive the Nobel Prize for science for "precision optical instruments and the spectroscope and metro logical investigations conducted herewith". Several versions of the interferometer were devised by Michelson including, the comparator for standardizing the meter, a mechanical harmonic analyzer for testing the harmonic motion of fringes, and a stellar interferometer for measuring the size of stars. Michelson died in 1931 decades before the laser would be invented. The interferometer is extremely sensitive to vibrations and should be isolated from them.

The figure below is a basic setup for an interferometer. The first component of the system is the light source. The light source can either be monochromatic or one with a range of wavelengths. When using a white light source there is a different interference fringe pattern for each frequency and the patterns wash each other out and produce a rainbow of fringes. A piece of compensating glass must be added to the setup when using white light sources. This is placed at 45^0 between the beam splitter and the fixed mirror.

This is added to ensure that each beam travels through the same number of glass surfaces. Most test setups will use a monochromatic light source such as a laser. It is easier to use a laser in the setup so there is only one interference pattern for one frequency of light. In order to meet the criteria for constructive interference the two paths from the beam splitter to each mirror must differ by a whole number of wavelengths, meaning bright fringes will be formed. When the distance differs by and odd number of wavelengths dark fringes are formed. Two formulas show this relationship where the difference of the two distances equals an odd or equal multiple of the wavelength of the light source.

P M 1 P - P M 2 P = p "e (bright fringes) P M 1 P - P M 2 P = (p/2) "e (dark fringes) The beam splitter is where the source beam is split up into the reference beam and the measured beam; it is also where they recombine before the screen. The beam splitter should be a 50/50 beam splitter such as a half-silvered glass plate. A piece of glass can be used but is not 50/50. There are two mirrors in the test set up, the fixed mirror and the movable mirror. Both mirrors should be highly reflective front surface mirrors. The movable mirror is attached to an accurately machined micrometer screw.

This allows the mirror to be moved to and from the beam splitter at a precisely determined amount. It can usually measure mirror movement of 2 um. If the difference of the two mirror distances is near zero, the fringes will be broad and widely spaced. If the path distance is large the fringes will be narrow and closely spaced. If the two mirrors are precisely aligned such that their planes exactly perpendicular to one another, the fringe pattern will consist of a series of concentric rings. When the movable mirror is moved to approach zero path difference, the fringe pattern will appear to collapse with all fringes moving toward the center and will disappear.

Ideal Interference Pattern The screen can be a variety of things including, a magnified image, an eyepiece, or a sensor network. Typically a magnified image is used. When the entire test set up is constructed two laser dots will appear on the screen. One of the mirrors can be adjusted so that the two beams are superimposed on each other. Then a lens with a short effective focal length (large gain) can be inserted in the path between the beam splitter and the screen.

This will magnify the interference pattern and the fringes will be easier to view and measure. A phototransistor can be placed in the screen to detect the transitions from a dark spot to a light spot it also can be connected to a counter through a Schmitt trigger to count the number of bright to dark transitions. The interferometer is a very useful and interesting laboratory tool and project. There are many uses for the interferometer from measuring the thickness of a human hair to the size of a distant star. The interferometer functions due to the interference between two paths of light. From this, extremely accurate measurements can be made to one half a wavelength of the light source.

Bibliography

McComb, Gordon 1988 The Laser Cookbook.
Tab Books: McGraw-Hill, Inc. New York. Hull, Daniel M. 1984 Center for Occupational Research and Development.