To find the wavelength of the light
Michelson Interferometer, mercury light source, counter.
The Michelson Interferometer is a precision optical instrument that splits a beam of light and allows each beam to follow different optical paths of lengths, L1 and L2, and then to recombine (the light beams) by superimposing them so that they interfere. If the difference in the path lengths traveled by the two rays, L2-L1, is an integral number wavelengths of the (monochromatic) light, then constructive interference occurs. If L2-L1 is equal to half a wavelength, then destructive interference occurs and no light is observed. A precision measurement of the path lengths L2 and L1 will allow a precision measurement of the wavelength of the monochromatic light used.
The actual interferometer to be used in this experiment is shown schematically
in Figure 1 below.
Figure 1. Michelson Interferometer
Light from source L is divided by the back surface partially- reflecting mirror M0, a portion being reflected to mirror M1 and a portion transmitted to mirror M2. After reflection from M1, and M2 , the beams arrive back at mirror M0 where they are partially transmitted and reflected to the eye. A part of each beam is reflected toward the observer at E, and if mirrors M0, M1, and M2 are properly adjusted, these two beams are precisely superimposed. The light that travels to M1 must pass through the glass of M0 three times while the light that travels to M2 passes through M0 only once. In order to compensate for the extra time delays in passing through the glass three times, the light that travels to M1 must pass through G ( a glass compensator of the same thickness and index of refraction as M0) twice. With the compensator G, each beam will be delayed the same length of time in traveling through the glass.
If the two beams that arrive at E are in phase, then they will reinforce each other and the observer will observe a high intensity light. If the two waves are out of phase then the observer will observe a low intensity light (darkness), since the waves will cancel each other. By moving one mirror or the other (M1 or M2) the waves' phase relaxation can be varied from "in phase" to "out of phase" and back again. This variation is caused by the change in path length traveled by one of the waves involved. If mirror M1, is moved back 1/4 wavelength, then the path from M0 to M1 and back to M0 is increased in length by half a wavelength, and the phase of the two waves changes from "in phase" to "out of phase" or vice versa. By counting the number of times the intensity fluctuates (bright to dark to bright is one "fringe") and measuring the displacement, L, of the mirror the wavelength can be determined:
where N is the number of fringes, L is the measured displacement of the mirror, and l is the wavelength of the light.N = L/(0.5l), (1)
The interference pattern that is observed will appear either as a bull's eye of alternating dark and light rings or as a series of slightly curved alternating dark and light bands. The vertical tilt of mirror, M2, will determine the pattern observed. The interference pattern will not be completely dark or light as might naively be expected from the simple discussion presented above. The light source provides a slightly divergent beam and each theoretical ray of light will follow a slightly different path giving a series of interference fringes (the bull's eye pattern). If M2 is not parallel to M1, the rays of light that strike the bottom of the mirror will travel a slightly different distance than those striking the mirror top, giving a series of parallel interference lines, much like the Newton's ring pattern shown in most physics texts.
In order to
increase the measuring accuracy of the interferometers used in this lab,
the micrometer that indicates the displacement of M1,
does so through a 5:1 mechanical advantage lever. All micrometer readings
are 5 times lager that the actual mirror displacement.
Exercise 1.
Place a green filter over the mercury lamps provided and then turn on the lamps. Place the lamp as shown in Figure 1 and observe the fringes at E. It is best to have the M1 to M0 and M2 to M0 distances nearly equal at the beginning. Each member of the lab team should practice moving the micrometer and counting fringes in order to learn how to grasp and release the micrometer without displacing the mirror. Mirror M2 has two adjustment screws that orient M2 relative to M1. Adjust these two screws until you obtain an interference pattern that is visually comfortable to you (as it moves).
Exercise 2.
Record the micrometer setting and count fringes for the micrometer knob always being rotated in the same direction. Do not count more than about 100 fringes at a time. Count fringes for the remainder of the lab period, trying to count at least 1000. When the counting is finished, read the micrometer setting and calculate the mirror displacement.
Exercise 2.
Calculate the wavelength using equation (1). What is the error?
Share your data with everyone else. Obtain the weighted statistical
class average and compare this wavelength with the accepted (not correct)
value in the CRC Handbook of Physics and Chemistry. Use the calculated
error in each wavelength measurement for the statistical weighting parameter.