Measure the refractive index of air using a Michelson interferometer.
- 1. Page | 1 EXPERIMENT NAME : MEASURE THE REFRECTIVE INDEX OF AIR USING MICHELSON INTERFEROMETER. INTRODUCTION: REFRACTIVE INDEX : The ratio of speed of light in vacuum to its speed in a specific medium. Refractive index, also called index of refraction, measure of the bending of a ray of light when passing from one medium into another. If i is the angle of incidence of a ray in vacuum (angle between the incoming ray and the perpendicular to the surface of a medium, called the normal) and r is the angle of refraction (angle between the ray in the medium and the normal), the refractive index n is defined as : ²The ratio of the sine of the angle of incidence to the sine of the angle of refraction²; i.e., n ꞊ sin 𝑖 sin 𝑟 Refractive index is also equal to the velocity of light c of a given wavelength in empty space divided by its velocity v in a substance, or n ꞊ c v
- 2. Page | 2 MICHELSON INTERFEROMETER : The Michelson interferometer produces interference fringes by splitting a beam of light so that one beam strikes a fixed mirror and the other a movable mirror. When the reflected beams are brought back together, an interference pattern results. The Michelson interferometer (invented by the American physicist Albert A. Michelson, 1852– 1931) is a precision instrument that produces interference fringes by splitting a light beam into two parts and then recombining them after they have traveled different optical paths depicts the interferometer and the path of a light beam from a single point on the extended source S, which is a ground-glass plate that diffuses the light from a monochromatic lamp of wavelength λ . The beam strikes the half-silvered mirror M, where half of it is reflected to the side and half passes through the mirror. The reflected light travels to the movable plane mirror M1 , where it is reflected back through M to the observer. The transmitted half of the original beam is reflected back by the stationary mirror M2 and then toward the observer by M.
- 3. Page | 3 Because both beams originate from the same point on the source, they are coherent and therefore interfere. Notice from the figure that one beam passes through M three times and the other only once. To ensure that both beams traverse the same thickness of glass, a compensator plate C of transparent glass is placed in the arm containing . This plate is a duplicate of M (without the silvering) and is usually cut from the same piece of glass used to produce M. With the compensator in place, any phase difference between the two beams is due solely to the difference in the distances they travel.
- 4. Page | 4 DISCUSSION OF APPARATUS : THEORY AND BACKGROUND : Michelson interferometer is utilized for very sensitive changes in gas concentrations, extra small distance changes, variations in refractive index, etc. Principle lies in splitting the beam from the laser source in the Beam Splitter (BS) by a ratio of 50:50 (in %) into two branches. Beam passes through both branches, while in one environment with varying index change is placed – in our case the air. Beams reflect from mirrors M1 and M2 back to the beam splitter. There they split again. From the observers point of view the part of both beams at the screen is important. According to phase difference, interference maximums and minimums appear. In case of lens inclusion right after the laser, the focused beam expands into an interference pattern, where its interference fringes change according to phase difference.
- 5. Page | 5 The two beams arriving at the screen produce an interference pattern. An interference pattern is normally a series of bright and dark concentric circles (Figure 2), because of the imperfections in the mirrors of our interferometers, the circles may be distorted. In the bright regions of the pattern, the crests of the waves of the two beams arrive together. In the dark areas the crest of one wave arrives at the same time as the trough of the other. If the optical path length of one beam changes by one wavelength, the interference pattern is shifted by one fringe. The optical path length is equal to nL, where n is the Index of refraction and L is the physical path length. The optical path length can be varied by changing either n or L. In our experiment the one beam passes through the cell of length L. Because the beam passes through the cell twice, the optical path length is 2nL. The air will be removed from this cell, changing the refractive index, n. The other beam passes through the same length of air, but with no cell in that beam, the pressure will remain constant. If the refractive index changes by ∆n, the path length changes by 2 ∆n L. As the air is removed, the pattern will shift by one fringe at each time the refraction index changes by an amount ∆n = λ/2L. A shift of m fringes will occur when the refractive index changes by an amount ∆n = mλ/2L The refractive index for most gases is close
- 6. Page | 6 to 1. For air and other ideal gases, the difference between the refractive index and 1 is proportional to the pressure of the gas. Thus we define the refractive index of air n = 1 + k p, where p is the air pressure and k is an unknown constant. When the pressure is changed, the change in the refraction index is ∆n = k ∆p. We can therefore relate the number of fringes shifted, m, to the change in pressure ∆p = ∆n/k = mλ/2Lk. Therefore the unknown constant, k, is given by k = mλ/2L∆p. Thus if you measure m fringes while the pressure changes by an amount ∆p, you can calculate the refraction index of air at room temperature using n = 1 + mλp/2L∆p WORKING PRINCIPLE : The Michelson interferometer operates on the principle of division of amplitude rather than on division of wavefront. Light from a light source strikes the beam splitter (designated by S) and is split into two parts. The beam splitter allows 50% of the radiation to be transmitted to the translatable mirror MI. The other 50% of the radiation is reflected back to the fixed mirror M2. Both these mirrors, MI and M2, are highly silvered on their front surfaces to avoid multiple internal reflections. The compensator plate C is introduced along this path to have the same optical path length when MI and M2 are of same distance from the beam splitter. After returning from MI , 50% ofthe light is reflected toward the frosted glass screen. Likewise. 50% ofthc light returning from tvb is transmitted to the glass screen. Thc two beams arc superposed and one can obser.e the interference fringe pattern on the screen. The character of the fringes is directly related to the differcnt optical path lengths travcled by the two bcams and. thcrcforc. is relatcd to whatevcr causcs a diffcrcncc in thc optical path lcngths. If two beams emanate from a common source, but travel over two different paths to a detector, the field at the detector will be determined by the optical path difference, which we will denote by : ∆𝑋 = 𝑋1 − 𝑋2
- 7. Page | 7 EXPERIMENT THEORY: The Michelson interferometer setup used in this lab consists of two mirrors (one stationary, one adjustable), a beam splitter, and a light source. Fine adjustments to the mirror (to within one micron) are made in this experiment using a micrometer. The purpose for the Michelson interferometer configuration is to produce noticeable interference patterns by splitting a light source into two separate beams. One of the beams of light is reflected by the fixed mirror into a device or in the case of this experiment, onto a surface (wall). The other beam is reflected by the movable mirror onto the wall.
- 8. Page | 8 A distinguishable interference pattern results when both of the light beams are brought together. These interference patterns are characterized by fringes, and they can be counted or measured for analysis as is done in this report. Experiments were conducted in this lab to understand the uses and capabilities of the Michelson interferometer, to measure the wavelength of a laser light, and to measure the refractive index of air. PROCEDURE: 1. According to Fig.3 construct the experimental setup. 2. Align all components in the same height. 3. Set the beam splitter in angle of 45° in respect to the source in such a manner that both 4. beams are perpendicular to the optical table. 5. Align the inclination and face of mirrors M1 and M2 so, that reflected beams overlap on the 6. screen. 7. Set pressure in the air chamber on maximum (40kPa), which corresponds to ∆P. 8. Slowly decrease the pressure and mark number of maximum-minimum changes in a selected 9. spot of the interference pattern. 10. Repeat steps 6.-7. several times and average obtained values. 11. Calculate refractive index of air according to (7).
- 10. Page | 10 RESULT ANALYSIS : The set of experiments performed in this lab were conducted to familiarize oneself with the various uses of a Michelson interferometer. The wavelength of light source can be determined using the Michelson interferometer configuration, and in the case of the experiments performed in this lab, the laser light being utilized was determined to have a wavelength of 643 ± 50 nm. Also, the refractive index of gases can be determined with a Michelson interferometer. The refractive index of air (n–1) was determined by the experiments performed in this lab to be 0.000192 ± 0.000025. The table below shows the conclusive data found in the experiment for the refractive index of air. This table shows the average ( n-1 ) values and standard deviations for each series. Also shown are the total averages of both the average (n-1) values and the standard deviations.