Determination of wavelengths and indices of refraction with the use of the interferometer "Experiments of physics"

As friends are lovers of science in particular of physics, today I want to change the subject of my publications a little and instead of talking about semiconductors, I want to show you an experiment very used in the undergraduate physics career, this experiment is done in my subject called "advanced optics laboratory". Below I present my detailed report with theoretical bases with their respective equations to use and likewise the experimental part.

Abstract

Interference is a phenomenon resulting from the interaction of two or more waves in space, this can occur in a constructive or destructive way, which increases or decreases its intensity at a point in space. Interferometry is a technique that uses the constructive interaction of light waves in order to achieve an increase in the object that is observed for its study, the instrument determined for this purpose is an interferometer. In the present investigation, this instrument is used in order to determine the wavelength of a laser using the Michelson and Fabry-Perot interferometers, as well as to determine the refractive index of glass and air with the Michelson interferometer.

THEORETICAL FUNDAMENT

Interferometry is used to obtain larger scale images for study, the technique combines light waves using the interference principle so that luminous beams in phase shift overlap constructively to form a suitable image.

The rise in the interest of the study of this type of phenomena arises at the end of century XIX, with attempts to illustrate the way in which the light can travel through the space and to give an explanation of the variation of its speed in the earth, for then the way to prove it was by assuming a medium in which the wave called "ether" could be propagated, which was responsible for that variation.

In 1881 Michelson designed an interferometer as a means for the existence of the ether, due in part to his efforts the ether is no longer considered a viable hypothesis.

But beyond that, the Michelson interferometer has become an instrument used to measure the wavelength of light, to use the wavelength of a known light source and to measure extremely small distances, and for the optical media research.

Figure 1. Schematic representation of the Michelson interferometer.
http://engineering.eckovation.com/jee-physics-notes-wave-optics/

Figure 1 shows a Michelson interferometer diagram. The laser light beam strikes the beam splitter, which reflects 50% of the incident light and transmits the other 50%. One beam is transmitted to the moving mirror (M1), the other beam is reflected towards the fixed mirror (M2). Both mirrors reflect the light directly towards the beam splitter. Half the light from M1 and half the light M2 is transmitted through the beam splitter for display on the screen.

The display of an interference pattern on the screen is justified because the beam of light being reflected in the moving mirror, redirected to the beam splitter and from this to the adjustable mirror and back, is for the purpose of changing its phase by the variation of its optical path length (LCO), this is defined as the distance traveled at the speed of light in vacuum, at the time t used by the light to travel the distance l in a medium with index of refraction n, that being aligned of their interaction results in an interference pattern visualized on the screen, which can change as this LCO is varied, a function that complies with the variable mirror, causing the interference pattern to form concentric circles show the valleys and the crests of this pattern that approach or move away from its center.

These fringes or interference rings are very sensitive to the slightest optical path variation of either beam. This is because the passage from a maximum to a minimum of interference occurs for a phase change of p rays from one beam to the other, which corresponds to an optical path variation of λ/2. Since l is of the order of tenths of a millimeter (632.8 nm for the He-Ne laser), it means that the interference pattern changes with very small variations of the optical path, even with small vibrations of the ground. For this reason interferometers often require anti-vibration tables, especially if they are to be used to make some kind of precision measurement. For the wavelength, slowly moving the mirror by a distance d_m and counting the number m of bands passing through a fixed point on the screen, the wavelength λ of the light can be calculated as:

On the other hand, it is demonstrable by this arrangement the refractive index of the glass knowing that:

Where N is the number of lines measured between angular variations, λ_0 is the wavelength in vacuum, t is the thickness of the glass is of (0.0053m) and ɵ is the angle of rotation of the glass.

Also useful is this arrangement to calculate the refractive index of air, it is analytically as follows:

Where ni and nf are the refractive indices of air at pressures pi and pf respectively and d is the length of the vacuum cell (3.0 cm).

EXPERIMENTAL METHODOLOGY

In order to carry out this experiment, the following implements were used: an interferometer, an adjustable mirror, a movable mirror, 18mm and 48mm distance lenses, a display, light scatter, helium-neon laser, vacuum pump, glass.

Figure 2. Model of the Michelson interferometer used in the Photonics Laboratory of the University of Zulia.
http://physical-optics.blogspot.com/2011/06/michelsons-interferometer.html

First, the light beam is calibrated as described above, verifying that the beam emitted by the laser with which the movable mirror is reflected is aligned, and with the aid of the adjustable mirror obtain the highest possible sharpness of the interference pattern on the screen.

Next, the experiment is set up according to the Michelson form, adjusting the scale at 0 of the micrometric screw and starting from there counting the number of lines passing over a reference point previously located, this to determine the wavelength of the beam by means of equation (1).

The second experiment calculates the index of refraction of the glass, for this a glass plate with a known thickness is located, in this case it is of (0.0053m), fixed to a rotating support in graduated scale, and also takes note of the number of strips passing through a point referenced as a function of the angle of rotation of the glass and by equation (2) to obtain a value for this index of refraction.

The third experience is the assembly to calculate the refractive index of the air, for this there is a vacuum chamber with a gauge scale that is located in front of the movable mirror, in this case note the stripes passing through a reference point as the internal pressure of the chamber changes, taking these data and calculating with equation (3) we can have an estimate of the refractive index of the air.

RESULTS AND ANALYSIS

Michelson interferometer:

First, the wavelength of the laser is obtained experimentally, taking measurements of the stripes that pass in point by varying the distance of the movable mirror with the micrometric screw. The results obtained are shown in table 1.

Table 1. Results obtained for λ with the Michelson interferometer.

Thus obtaining an experimental value of the wavelength of the laser as:

With a discrepancy with respect to the registered value of 4.45%.

Then, the same configuration of the Michelson interferometer is used to calculate the refractive indexes of the glass and air. For the first, the data obtained from the number of stripes passing through a point are recorded as a function of the rotation of the glass located between the beam and the movable mirror and by equation (2) to obtain experimentally the refractive index of the glass. For the second, the data obtained from the number of stripes passing through a point is recorded as the pressure is varied inside the vacuum chamber using the pump with gauge scale and using equation (3) to obtain experimentally the refractive index of the air.

The results obtained from this experiment are shown in the following tables.

Table 2. Results obtained for the index of refraction of the glass.

Table 3. Results obtained for the refractive index of air.

As a result it is obtained that for the refractive index of the glass the experimental measurement is:

With a discrepancy from the current register of 13.85%. Also for the index of refraction of the air the experimental measurement is:

With a discrepancy from the current record of 8.16%.

CONCLUSIONS AND RECOMMENDATIONS

We have concluded all the experiments which successfully achieved the proposed objective, thus showing the application of interferometry to calculate useful physical variables. However, it should be noted that measurement errors can be reduced, recommending a better alignment of the laser with respect to the moving mirror, thus obtaining a tighter calibration and better visibility of the interference pattern, it is also advisable to design a graduated scale that fits in good shape to our vision to comfortably locate a point of reference.

REFERENCES

• Eugene Hecht "optics" Madrid. Year 2000 Editorial Addison Wesley iberoamericana. P: 73.

• Instruction Manual and Experiment guide for the PASCO scientific models OS-6255A thru OS-9258A.

• http://www.fceia.unr.edu.ar/fisicaexperimentalIV/CATEDRA/Interferometro%20de%20Michelson.pdf

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I hope you have enjoyed my experiment, if you have any doubts on the subject remember to leave your comment and my person will kindly try to clarify those doubts.

Carlos Pagnini