The Michelson Interferometer

Authorship: Partha Chinnasamy, Jacob Weitting

Department of Physics and Astronomy, AugustanaCollege, Rock Island, IL61201

Abstract: After devising experiments to prove that light has finite velocity, science community was determined to understand more about the nature of light. The wave nature of light was understood by interference. Michelson found a method where distance can be expressed in terms of wavelength using interference patterns of light. This experiment can be used to determine wavelengths or measure displacement with known wavelengths. Green diode laser and Sodium vapor lamp were used for our experiments. The green diode laser had a fringe spacing of 283 nm ± 25 nm and found to have wavelength of 566 ±25 nm. Similarly the sodium source had fringe spacing of 281± 25 nm with wavelength 562 ± 25nm. The D lines of Sodium found to have wavelengths 562.3nm and 561.7nm ± 25nm

I. Introduction

The velocity of light is so great it evaded experimental measurement until 1675 [1]. Danish astronomer Olaf Roemer had used measurements of the eclipse times of satellites in Jupiter to obtain a number for the speed of light(2.1 x 108m/s). In 1849 the first terrestrial measurements of light velocity was made by French scientist Fizeau. He obtained a value of 3.15 x 108 m/s. Albert A Michelson made precise measurement of light using Foucault method and obtained a value of 2.99774 x 108 m/s. The wave nature of light was understood by his newly invented interferometer which can precisely measure displacement in terms of wavelengths of a light source. This method is considered to be a major breakthrough in precision measurement.

With an optical interferometer one can measure physical distances directly in terms of wavelengths of light by counting interference fringes that move when one or the other of two objects are displaced. The beams must be mutually coherent for fringes to be seen. There must be a definite phase relationship between them. Mutual coherence is obtained in the Michelson interferometer by splitting light that originates from a single source with a partially reflecting mirror known as a beam splitter (BS). The reflected (R) and transmitted (T) waves are redirected by ordinary mirrors to the output where they are superposed to form fringes. This process is known as interference by division of amplitude.

II. Experimental Setup

The light from a source, S, is divided by a 50% Beam Splitter (B) oriented at 45 degrees to the beam. The transmitted beam travels to mirror M1 where it is back reflected to B. 50% of the returning beam is deflected by 90 degrees at B and it then strikes the screen, E .The other 50% is transmitted back towards the laser and which is not relevant to our experiment. The reflected beam travels to mirror M2 where it is reflected. Again, 50% of it then passes straight through B and reaches the screen. The two beams that are directedtowards the screen, E, interfere to produce fringes on the screen.

A linear optical equivalent of the Michelson helps to understand the optical path differences.First, replacing mirror M1 with its virtual image, M1’ isseen when looking into the beam splitterfrom the laser. The laser aperture, S, is then replaced by its virtual image, S', as seen looking intoB from the position of M2. The fringes are the same as would be generated by a single source,S', that is reflected from two distinct mirrors, M2 and M1', separated by a distance d. If mirror M1 is moveable, the optical path difference is 2d between the raysreflected from M1' and M2. The center of the screen is bright when the optical path difference is an integral number of wavelengths.

The condition for a maximum of intensity at the center of the screen is:

2dn

Where,

 / = / wave length(nm)
d / = / optical path difference (in)
n / = / no of fringes

Figure 1. The MichelsonInterferometer

III. Results

The green diode laser had a fringe spacing of 283 nm ± 25 nm. The measurements were taken counting twenty fringes and the distance traveled was recorded. Using equation 1 the wavelength was found to be 566 ±25 nm. The actual valued is 532 nm.

The second experiment was done using Sodium vapor lamp. Since Sodium source produces light waves with two different wavelengths (also known as D lines),using the same procedure we obtain only an average wavelength. The fringe spacing of 281± 25 nm is observed and the average wavelength was found to be 562 ± 25nm.

Using followingequations wecan solve for and values.

2)

(3)

Solving above equations the D lines of Sodium were found to be 562.3nm and 561.7nm ± 25nm. The actual values of D lines are D1= 589.592, D2= 588.995

IV. Discussion

It can be found that the values obtained in this experiment are within range of the current experiment setup measurement capability. We need more accurate methods in order to obtain more precise values.The measurement system had an error of 25 nm.

V. Conclusion

Wavelengths of two light sources were measured using Michelson Interferometer.The green diode laser had a fringe spacing of 283 nm ± 25 nm and hence found to have wavelength of 566 ±25 nm. Similarly the sodium source had fringe spacing of 281± 25 nm with average wavelength of 562 ± 25nm. The D lines of Sodium were found to have wavelengths 562.3nm and 561.7nm ± 25nm

References

[1]F.W. Sears,Principles of Physics III optics. Addison-Wesley Press, Inc 1945

Good! Discuss the measurement of D, and how that determines the difference in wavelengths. Give sources for standard values. Any ideas for more accurate methods?