# PHY105 Physics Lab Experiment Proof Reading Services

## Introduction

This paper tends to give a brief introduction on the interferometer which was invented by Michelson Morley. It provides a brief history on interferometer and how it is significant. Besides, various equations related to the operation principle of an interferometer is elaborated as well as a psychologyexperiment which proves that the various properties of light can be utilized in making very small measurements. In the 19thcentury,there was a tough debate about the existence of a certain medium that enabled the propagation of light known as luminiferous aether. This medium explained the ability of light based on principles of a wave to propagate through a vacuum, a phenomenon that contradicts the potential of waves [1].

It was until the late 1800s that this debate terminated by the invention of the interferometer, a device that combines two or more sources of light with the purpose of developing an interference pattern that can be determined and analyzed. These investigative tools generated patterns which contained data with regards to the phenomenon or object under study. Besides, insignificant measurements which prove difficult to determine can also be determined by this tool. The interferometer comprised of a beam splitter, photodetector, series of mirrors and a laser which records the interference pattern. When the various particulars of light are known, an introduction of variations in the beam path can assist in analyzing the effects of the introduced interference pattern [3].

Additionally, the phase relationship between two interfering beams provides the characteristics of the fringe pattern. Usually, this phase relationship can be varied by either changing the distance between the two interfering beams or changing the medium of interference.

### Theory

Generally, light is considered as a transverse wave. When lights having the same amplitude and wavelength travel in the same medium, their amplitudes combine therefore resulting into an overall wave with either lesser of greater amplitude. This superimposition is what is known as interference and one that Michelson applied in the coming up of the interferometer. When the resulting wave is greater, it means that the interference was constructive and when it is comparatively lesser, then it was a destructive interference and usually brought about by the adding of one crest of a wave with another trough of a different wave.

### Constructive interference

In this kind of interference, the path difference of the beams is usually an integral multiple as demonstrated by the below equation

Path difference =..................................................................................................(1)

Where m is the order, i.e.m =0, 1, 2...

λ =wavelength,

Destructive interference

In destructive interference, the path difference is given by

Path difference = (m+ 0.5)λ ...................................................................................(2)

i.e.

With the aid of this device, distance can be directly determined in terms of the wavelength of the light that was used, a beam splitter helps in splitting the beam of light which comes from one human resource thereby resulting to coherent beams which are then redirected by the use of ordinary mirrors into a screen where they’re superimposed to come up with g=fringes. Consider the Michelson- Morley diagram below, [2]

Light from the single sources s gets split by the beam splitter BS that is sloping at 45 degrees in order to generate beams with the same intensity. The beam that is transmitted T travels to the first mirror M1 and then is reflected back to BS. The beam splitter then reflects 50% of the reflected beam that in turn strikes screen E. It is then reflected by r and then travels to the second mirror M2 that reflects it, permeating 50% of the beam to pass to the beam splitter and reach the screen. It will be noticed that the light ray that undergoes reflection at the second mirror M2 passes the beam splitter thrice as opposed to the one reflected at m1 that only passes once [4].

The refraction index of the glass plates determines the optical length since it causes an optical path difference between the beams. Introducing a glass plate between the splitter and the first mirror helps in compensating for this. The glass plate must have the same refractive index and thickness as BS. Hence, the beams which recombine will interfere and generate fringes on the screen e. the nature of interference is determined by the relative phase of the two beams. When the inclination of the two mirrors, M1 and M2 are adjusted, various shapes of fringes are produced i.e. curved, straight line or circular fringes.

Therefore, one is in a position to directly see a virtual M1 and original M2 which has been formed by the splitter in the diagram below. Implying that the interfering beams have emanated from virtual M1 and original M2. When the length of interferometer arms are equal, then m2 will coincide with virtual m1 [6].

If not, then :

Assume the distance between them to bed, and considering light ray from s, the reflection will be by both m2 and m1 virtual, thereby resulting in reflections s1 and s2. The separation distance will be 2d. Assuming the inclination angle to beθ,the path difference of the beams will thus be [5]

Path difference =2dcosθ. .................................................................................... (3)

When the splitter reflects a light from M1, there’s variation in the phaseπ, corresponding to the path difference, λ/2.

Therefore, total path difference =

In constructive interference,............................................ (4)

.............................................. (5)

In destructive interference, the path difference is [8]

.................................... (6)

From the above theory, the wavelength of light by use of the Michelson interferometer can be determined by the following equation.

............................................................................................. (7)

### Discussion

From the data obtained, it can be noted that there was a slight variation for each of the trials made in the determination of the wavelength. The allowance between the average value and the initially obtained results was quite insignificant hence proving the Michelson equation of determining the wavelength. Besides, the values obtained from the Fabry-Perot mode also demonstrated a high level of similarity, which was expected [7].

Additionally, the slope of the n vs. pressure graph for air was found to be linear, hence implying that the refractive index is dependent on the atmospheric pressure.

#### References

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[2] Jha R, Villatoro J, Badenes G. Ultrastable in reflection photonic crystal fiber modal interferometer for accurate refractive index sensing. Applied Physics Letters. 2008 Nov 10;93(19):191106.
[3] Kersey AD, Marrone MJ, Davis MA. Polarisation-insensitive fibre optic Michelson interferometer. Electronics letters. 1991 Mar 14;27(6):518-20.
[4] McKenzie K, Shaddock DA, McClelland DE, Buchler BC, Lam PK. Experimental demonstration of a squeezing-enhanced power-recycled Michelson interferometer for gravitational wave detection. Physical review letters. 2002 May 23;88(23):231102.
[5] Tian Z, Yam SS, Loock HP. Refractive index sensor based on an abrupt taper Michelson interferometer in a single-mode fiber. Optics letters. 2008 May 15;33(10):1105-7.
[6] Wang P, Brambilla G, Ding M, Semenova Y, Wu Q, Farrell G. High-sensitivity, evanescent field refractometric sensor based on a tapered, multimode fiber interference. Optics letters. 2011 Jun 15;36(12):2233-5.
[7] Wang YJ, Anderson DZ, Bright VM, Cornell EA, Diot Q, Kishimoto T, Prentiss M, Saravanan RA, Segal SR, Wu S. Atom Michelson interferometer on a chip using a Bose-Einstein condensate. Physical review letters. 2005 Mar 11;94(9):090405.
[8] Wu D, Zhu T, Deng M, Duan DW, Shi LL, Yao J, Rao YJ. Refractive index sensing based on Mach–Zehnder interferometer formed by three cascaded single-mode fiber tapers. Applied optics. 2011 Apr 10;50(11):1548-53.