Reference no: EM131100150
Experiment - The Michelson Interferometer
Prelab Questions
1. Show schematically how an extended source implies circular fringes.
2. Show how Eq. 7 implies circular fringes.
3. It is possible to view interference fringes from a white light source if the path length difference is very small. When viewing white light fringes, which colour should appear on the outside of the circular fringes and which colour on the inside?
4. In Part 3 of the experiment, you are asked to determine the mean wavelength and the separation of the sodium doublet. There are now two sets of fringes, one for each line of the doublet. You will see fringes due to both when they constructively interfere, and the fringe pattern will disappear when they destructively interfere. Once you have determined K it should be obvious how you determine λ¯. (How will you do this?)
Determination of ?λ is a little more subtle. Show that the mirror distance between two positions where the fringes disappear is given by
2(d1 - d2) = λ1λ2/λ1 - λ2
Experiment
1. Investigate the operation of the apparatus. Obtain an interference pattern using the sodium light source, which consists mainly of two yellow wavelengths (known as the sodium doublet). Make the distance AM1 and AM2 roughly equal and use a sighting pin during the initial mirror tilt adjustments. The fringes should be circular and centred, rather thick and of good contrast. (Please look at the figure in the Beck Manual.)
2. Determine K. Using the mercury light source (green), calibrate the carriage movement. Assume the wavelength of the green mercury light to be 546.07 nm.
3. Determine the mean wavelength of the sodium doublet and the separation of the two lines.
4. Determine the refractive index of air. Measure the difference in optical pathlength that occurs as air is removed from the vacuum cell using the vacuum pump provided.
5. (Optional) White light fringes can be observed with the Michelson interferometer when the optical path difference of the interfering beams is nearly zero. Observe the striking colour changes in the pattern as the path difference is slowly varied from zero. (Ref. 4, and Appendix to this handout.)
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