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Introduction:-. Laser light are assumed to be monochromatic light. They are not so
monochromatic but its wavelength is spread over a small range and centered on a wavelength which is called wavelength of source. Wavelength is an important parameter of laser. Laser applications requires laser of specific wavelength. It is a well-established fact that different dental procedures require different laser wavelengths. Wavelength is important because specific body tissues interact in unique ways depending on the particular laser source. So laser wavelength is an important parameter. It is found mostly by Michelson Interferometer.
Michelson interferometer:- Michelson Interferometer was introduced by Albert
Michelson in 1881,is an instrument that brought the era of modern physics; most notably, it validated Einstein's theory of special relativity and dismissed the presence of ether through which light was thought to have propagated. The Michelson interferometer is a precision optical instrument that splits a beam of light and allows each beam to follow different optical paths of lengths, L1 and L2, and then to recombine (the light beams) by superimposing them so that they interfere. If the difference in the path lengths traveled by the two rays, L2- L1, is an integral number wavelength of the (monochromatic) light, then constructive interference occurs. If L2-L is equal to half a wavelength, then destructive interference occurs and no light is observed. A precision measurement of the path lengths L2 and L1 will allow a precision measurement of the wavelength of the monochromatic light used.
Figure 1. Michelson interferometer
Figure 1 shows the Michelson Interferometer. Light from the source passes through the beam splitter, divides the light along two paths. One part is transmitted to mirror M 1 the other is reflected to mirror M2. These two rays reflect back to the beam splitter where they recombine and proceed toward the eyepiece where interference is observed.
A micrometer is provided which allows movement of M2 and a pair of screws on the back of M allows for its adjustment in two perpendicular directions. If M1 and M 2 are adjusted such that light reflected from both mirrors recombine while traveling towards screen. The mirrors are capable of moving forward and backward with the help of fine screws marked with scale to find position and distance travelled by mirror. They can also rotate so that both beams can be made such that either they recombine with zero angle between or with some arbitrary and adjustable angle.
Light reflected from both mirrors have great chance that they might have travelled different distances. This variation is caused by the change in path length traveled by one of the waves involved. If mirror M 1 , is moved back 1/4 wavelength, then the path from beam splitter (BS) to M 1 and back to BS is increased in length by half a wavelength, and the phase of the two waves changes from "in phase" to "out of phase" or vice versa. Each time when beams are out of phase, there will be a dark fringe on screen and vice versa. By counting the number of times the intensity fluctuates (bright to dark to bright is one "fringe") and measuring the displacement, L, of the mirror the wavelength can be determined:
Where N is the number of fringes, L is the measured displacement of the mirror, and λ is the wavelength of the light. So using this formula we can calculate wavelength of source. Formation of Fringes:-. Fringes are formed from interference of two beams when the two beams are emitted from the same source. Let a source of monochromatic light. This monochromatic light can be regarded as a series of sinusoidal wave-trains as shown in figure 2 and between each two trains there is some random phase change. Each wave train has constant phase relation in same wave train but no phase relation with other wave train. The average length of the wave-train between these interruptions (e.g. the distance l in Figure 2) is called the "coherence length" of the light, and is of order one meter for ordinary light sources and this type of coherence is called temporal coherence.
Coherence length can be expressed as the product of the number of waves, N, contained in the train with their wavelength which is given by
s= l = Nλ
By a simple extension of this concept, the "coherence time" is defined as the coherence length divided by the speed of light in the medium.
Where c is the velocity of light, and the length of time interval t is called the coherence time. It follows that the coherence time is usually in the range 10-9^ to 10-8^ sec.
If light from two similar sources is combined, there is a great chance that time delay between two beams is such that the fringe pattern (positions of maximum and minimum intensity) will undergo random jumps every 10-9^ sec or so, and fringes will not be observed. However, when the
Fig. Fringes produced on screen
- Counting fringes:-. Now, starting from any point, move one of the mirrors slowly and count the fringes changing with mirror motion on screen. Count about 100 fringes and note distance travelled from micrometer fixed with mirrors.
- From fringes counted, wavelength of source can be calculated as
Where N is number of fringes counted, L is length through which mirror moves and λ is wavelength on light.
Observations:- During experiment, we observed some important phenomena’s.
- Placing and rotating polarizer in front on laser light, changed intensity of light of light on screen which showed that laser source is polarized laser light source.
- Fringes formed on screen were perpendicular when beams after reflection made angle in horizontal plane and vice versa.
- Light on screen were not so uniform, even for single bright fringe on screen, light were not looking uniform. The reason for this is, as we know there is no one screen which is perfectly smooth, so is screen of experiment too. So light reflected from rough screen has some phase differences and they interfere constructively or destructively so light on screen were not smooth but had some variations.
Wavelength measured by Michelson interferometer
Length (μm) Fringes λ measured λ - λ 0 (λ 0 0.6328μm)
30 97 0.61^855 - 0.022%
35 110 0.636364^ 5.63E-3%
128 0.625 - 0.0123%
