The Michelson Interferometer Mitch Musgrove, Edgar Valle, Ahmed Abuzant Department of Physics and Astronomy, Augustana College, Rock Island, IL 61201 Abstract: The Michelson Interferometer is an apparatus that is used to measure lengths and changes in lengths with great accuracy through the use of interference fringes. In this experiment we used the Michelson Interferometer along with some basic wavelength equations to calculate the wavelength of a red diode laser and also a sodium light source. We also used the device to determine the difference between the 2 similar wavelengths emitted from the sodium light. Average calculated wavelength of the red diode laser was found to be 660±82.635nm. Average calculated value of the sodium light wavelength was found to be 600±47.729. Difference between 2 slightly wavelengths of light emitted by sodium light ____?____. I. Introduction The purpose of this lab was to determine the wavelength of two different light sources (A diode laser and a sodium light), with the use of a Michelson Interferometer and the equation . We also used this device to determine the small difference in wavelength of the two waves emitted by the sodium light using the equations and . For the Diode laser we found an average wavelength of 660±82.635 nanometers and for the sodium light we found an average wavelength of 600±47.729 nm. For the two wavelengths of the sodium light we found a difference in wavelength of ____?____. II. Experimental Setup Figure 1 – The Michelson Interferometer To acquire data for this lab we used a Michelson Interferometer. Before we could begin to take data we had to align the components in our setup. As seen in figure 1. The diode laser was set to strike the center of moveable mirror M1 so that the laser would reflect directly back into the laser. Next the beam splitter was positioned at a 450 angle to the beam to reflect part of the beam to adjustable mirror M2 near its center. This placed 2 dots on the viewing screen. Now the beam splitter is again adjusted until the 2 dots on the viewing screen are as close together as possible. Finally, use the thumbscrews on the back of M 2 to adjust the mirror until till the two dots are directly on top of each other. Once everything was in alignment a converging lens is used to project an interference pattern onto the viewing screen. Further adjustment of the mirrors may be needed to produce circular fringes that are not too closely that are not too closely spaced. To take data we marked a dark fringe on the viewing screen and moved the micrometer attached to M 2 in order to move across 10 fringes. This movement of the mirror was read off of the micrometer scale to provide us with d which we then used the equation to calculate wavelength. For the sodium light everything was done the same as the laser except for instead of the use of a converging lens and a viewing screen we looked directly into the apparatus and used our own eye as the viewing screen. For the measurement of the wavelength difference between the 2 sodium light lines we again looked into the apparatus, but this time we watched as the fringes went from very blurry to crisp back to very blurry. III. Results λ (nm) 760 700 660 660 640 680 640 640 Average 660 Error in λ(nm) 82.63517065 82.63517065 82.63517065 82.63517065 82.63517065 82.63517065 82.63517065 82.63517065 0 Figure 2 – Laser diode data of calculated wavelength and error. Average λ (nm) 740 640 580 580 580 640 580 680 580 580 580 580 620 600 580 600 Error λ (nm) 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 47.72939595 0 Figure 3 – Sodium light source data of calculated wavelength and error. In figure 2, we see the final calculated values of wavelength for the red diode laser with the average value at the bottom. These values were calculated using where d is the change in position of M2 as read from the micrometer. To calculate the error wavelength, we propagated error with the equation for uncertainty of a function with several variables (pg. 75 fig. 3.47 [2]) and standard deviation of our measured values of d. In figure 3, we have the same thing as figure 2, but for the sodium light source rather than the diode laser. Again error was calculated the same as for the laser in figure 2. Trial 1 2 3 4 5 6 Start 536.2 248.8 9.2 247.8 534.8 11.7 End 248.8 13.6 247.8 534.8 815 250.2 Average Part D (measured in microns) Δd D di di^2 287.4 574.8 -26.25 689.0625 235.2 470.4 25.95 673.4025 238.6 477.2 22.55 508.5025 287 574 -25.85 668.2225 280.2 560.4 -19.05 362.9025 238.5 477 22.65 513.0225 261.15 Sum 3415.115 STDEV Difference in λ 23.83664895 23.83664895 23.83664895 23.83664895 23.83664895 23.83664895 Figure 4 – data for calculation of wavelength difference between 2 different sodium light wavelengths (Incomplete) Figure 4 is incomplete due to our failure to understand and correctly use the equations provided, which are as follows and . IV. Discussion Our results for the red diode laser are look very promising with our average value for wavelength of 660±82.635nm as compared to the accepted wavelength of 750nm. This average exclude the very first data point because was very inconsistent with our other data points. This may have been due to switching direction with which we rotated the micrometer therefore bringing any free play in the micrometer into our error. The results we calculated for the wavelength of the sodium light were also very close to the accepted value of 589nm for sodium light. We found an average wavelength of 600±47.729 and only 4 of our 15 calculated values did not contain the accepted value within their error and 2 of these were less than 5 nanometers outside the calculated error. The final table in figure 4 is incomplete due to our inability to understand how to use the provided equations to determine the difference between the two different wavelengths emitted by the sodium light. References [1] Michelson Interferometer lab handout [2] Taylor, John R. An Introduction to Error Analysis: the Study of Uncertainties in Physical Measurements. 2nd ed. Sausalito, CA: University Science, 1997. Print.