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In essence, the Michelson interferometer consists of a beam splitter which divides a beam of light into two parts of equal intensity, one transmitted, the other reflected. These two Beams strike mirrors at practically normal incidence and return to the beam-splitter where they recombine. The basic arrangement is shown in Figure. Light from a source S is incident on a beam splitter. Half of the beam goes to the mirror M 1 and half goes to the mirror M 2. The beams in the Figure 1 recombine and fringes may be seen at detector position.
Figure 1 : Schematic illustration of a Michelson interferometer
Formation of Fringes
For fringes to be formed it is essential that the two beams be derived from the same source. This can be understood by noting that monochromatic light can be regarded as a series of sinusoidal wave-trains which are interrupted at frequent but random intervals as shown in Figure 2. During each interruption, the sine wave undergoes an abrupt phase change. 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. Coherence length can be expressed as the product of the number of waves, N, contained in the train and their wave length.
The formula for coherence length is then given by
s= l = N
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 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, 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 two beams are derived from the same source, both beams undergo these random phase changes but do so simultaneously so that the phase relation between them is unaffected. In this case, the interference fringes will remain stationary and can, therefore, be observed. On the other hand, it should be noted that if the difference between the optical path lengths of the two beams is larger than the coherence length, fringes will not be observed, even though the beams are derived from the same source.
.
Figure 2: Wave train from a laser.
We see that the centre of the fringe pattern has a maximum intensity if d = nλ/
Observations and Calculations
Distance(cm) Imax Imin
Visibility= I I Iback
I I
max min^2
max min
Table1: Data collected with photo detector for different path differences.
Fig. 3 the coherence length of He-Ne Laser.
Conclusion
From the above fig 3 we see that the coherence length is 48 cm. further increases in the curve is due to the longitudinal modes.
Visisbility Vs Distance for He-Ne Laser
0
1
0 10 20 30 40 50 60 70 80 Distance(cm)
Visisbility
Precautions
- The mirrors should be perfectly aligned.
- The detector should be placed at a reasonable distance.
- Photodetector should be used for scanning very precisely.
- Use the translation stage for better scan of fringes.
Sources of Error in the Experiment
In the above experiment following sources of error are observed:
Beam splitter used is not very efficient as it is observed the two component of light have some intensity difference. Alignment of the apparatus is also a source of error as if the reflected and transmitted components are not falling on a same point pattern will not be as much symmetric and clear. The input parameters affecting the interference pattern are uncertainties in and the refractive index of air (na). As index of air (na) is function of the air temperature t, the pressure p, the relative humidity H. However, the errors in measurements could be decreased by improving the environmental conditions. The inefficient way of scanning the fringes with Photodetector. Less sensitivity of Photodetector to collect the data at its input (photodiode).
