INTERFEROMETERS NOTE: Most mirrors in the apparatus are front surface aluminized. Do not touch the surfaces nor wipe them. they can be easily permanently damaged. Introduction This experiment provides three techniques for observing interference phenomena in light, and enables you to make various measurements using interference. A. Michelson Interferometer The Michelson interferometer is fully described in references 1, 2 and 3. Light from an extended source is separated into 2 paths by partial reflection from a semi-silvered mirror, and then recombined by the same mechanism, so that interference occurs. The particularly useful feature of this interferometer is the extend of separation of the paths, so that comparison of two very different types of optical paths may be made. There are 4 principal types of measurements that can be made with this type of interferometer. 1. Width and fine structure of spectral lines, 2. Lengths or displacements in terms of wavelengths of light, 3. Refractive indices, 4. Differences in the velocity of light along 2 different directions. In this experiment, several such measurements are suggested. You may try out whatever is of interest to you. Experiment 1 - Circular Fringes Set up the interferometer as described in references 1 and 3. Using either a Sodium or a Mercury vapour lamp (observe the fringes from both) adjust the mirror tilt screws and the micrometer position control so that the images of the two mirrors are parallel and so that circular fringes are observed. Move the micrometer position control so that the diameter of the fringes become largest. This implies that you are close to zero optical path difference between the two light paths. (Recall that zero difference produces a bright fringe across the whole field of view). Now using a white light source, observe white light fringes. The dark centre of the white light fringes will tell you the position of zero path difference. (Note the white light fringes are only observable over a region of about 20 fringes, corresponding to a total rotation of about 20 of the micrometer screw, so they are easy to miss).
Experiment 2 - Localized Fringes Starting with the adjusted apparatus of Experiment 1, and using first Mercury and Sodium light, and then white light, observe localized fringes by slightly changing the adjustment on the tillable mirror and then varying the micrometer position control. Experiment 3 - To Measure a Distance in Terms of the Mean Wavelength of Sodium Light View the circular or nearly circular fringes of sodium light. Traverse the mirror slowly by means of the micrometer screw counting the fringes which pass the edge of the field of view. Record the micrometer screw reading every 50 fringes and continue until about 1000 fringes have been counted. NOTE: The mirror carriage should always be driven towards the observer when making readings. Overshoot cannot easily be corrected by reversing the direction of rotation of the micrometer screw because of backlash between the screw thread and the carriage. Ask the demonstrator to explain this point if it is not clear to you. Plot a graph of the micrometer reading against number of fringes n passing the field. From this graph, and the mean value of the wavelength of the sodium lines you can obtain a calibration curve of micrometer reading against actual distance moved by the mirror. Comment on the uniformity of the micrometer screw thread. (See Reference 1 for the theory of this measurement). Experiment 4 - To Determine the Wavelength Difference for the Two Lines The sodium `line' is really a doublet of 2 wavelengths λ 1 and λ 2 having a small wavelength separation and different but comparable intensities. A fringe pattern is formed for each wavelength and the resultant seen is that produced by the superposition of these two patterns. For certain path differences (i.e. positions of the mirror) the bright fringes of the two patterns coincide and the resultant fringes pattern has good fringe visibility. For other path differences (intermediate between those for maximum fringe visibility) the bright fringes of one pattern coincide with the dark fringes of the other and the resultant fringe pattern has rather low visibility. Thus on moving the mirror back slowly, successive positions of the mirror for about 12 of each of these situations should be measured. From these readings the average distance between adjacent positions of the mirror giving maximum fringe visibility is obtained, and a similar value can be found for the positions of minimum visibility. Although each setting for maximum (or minimum) fringe visibility is probably not very accurate (since it is subjective) by making a large number of settings the probable error can be reduced. To calculate, the wavelength separation of the 2 sodium yellow spectral lines, consider λ 1 and λ 2 to be the 2 sodium wavelengths where λ 1 > λ 2. 2
Then if m is the change in order number at the centre of the field of view between consecutive positions of maximum fringe visibility for λ 1, then ( m + 1) is the corresponding change in order number for wavelength λ 2. If t is the average distance between the positions of the mirror for maximum fringe visibility. Then so 2t = m1 = ( m + 1) 2 1 1 2t( - ) = 1 2 1 - = 12 = 2 1 2 2t m 2 /2t = 1 1 m Experiment 5 - To Determine the Refractive Index of a Transparent Solid If a thin plate of thickness `d' of the transparent substance is placed in one beam of an interferometer the optical path difference is changed by ( - 1)d. (The refractive index of air being taken as unity). As a result the interference pattern moves through n fringes where Note that n is not necessarily a whole number. n = ( -1)d/ Unfortunately since all monochromatic fringes look the same we cannot recognise a sudden jump in the fringe pattern. This can be overcome by using white light fringes to locate the whole number of fringes moved. Set the moving mirror to give equal path lengths for the interfering beams using the mercury and then white light source. Note the reading of the micrometer for the mirror on the carriage. Interpose the transparent solid in one of the interfering beams, and compensate for this change in optical path difference by moving the mirror back or forward until white light fringes are central in the field of view again. Measure the new position of the mirror. 3
Experiment 6 - To Determine the Refractive Index of Air The principle of this experiment is the same as in Experiment 5. In this case the gas cell is placed in one beam path and the two compensating glass discs are placed in the other beam path to compensate for path differences introduced by the windows of the gas cell. By connecting the gas cell to a manometer and a vacuum pump and valves, the pressure of air in the gas cell can be measured. By counting fringes passing as the pressure is changed, the refractive index of air as a function of pressure can be measured. Experiment 7 - An Exercise in Appreciating the Michelson - Morley Experiment Considering the accuracy of measurement you were able to achieve in the above experiments, deduce what improvements in the performance of the apparatus would be needed to detect the moving aether effect in a Michelson-Morley experiment, assuming the aether theory were valid. Suggest ways you could obtain this improvement. B. Fabry-Perot Interferometer The Fabry-Perot interferometer is fully described in references 2, 3, 4 and 5. In this case, the interferometer consists of parallel semi-silvered glass plates, so that multiple reflections take place. This results in very narrow sharp interference fringes, allowing small wavelength differences to be measured. In particular, this interferometer has been used in the measurement of Zeeman effect and hyperfine structure os spectra. No set experiment will be described here. You are free to set-up the apparatus as described in reference 3, to observe the interference fringes, and if you wish, work out further experiments. C. Twyman - Green Interferometer This interferometer configuration provides a means of testing the true-ness and optical perfection of prisms and lenses. The technique, which uses a modification of the Michelson interferometer, is fully described in references 1, 2 and 3. We suggest that you set-up the interferometer as described in reference 3. Mercury light is convenient for this set-up. Test out one or two prisms and evaluate their optical uniformity. If you wish to see what a bad prism looks like, you can simulate this by placing a common slide glass in front of a good prism References 1. F.A. Jenkins and H.E. White, "Fundamentals of Optics 4th Edition", 271-282. 4
2. R.W. Ditchburn, "Light". 3. Ealing/Beck "Instructions for the description of the `Universal' Interferometer", (available at the wicket). 4. F.A. Jenkins and H.E. White, "Fundamentals of Optics 4th Edition", 301-308. 5. A.C. Melissinos, "Experiments in Modern Physics", 309-323. J.V. 6/82 Rev. 5