Interferometry

Introduction: Sometimes 'no' is the right answer. In the late 19th century the search was on for the medium that carried light waves. Called the luminferous ether or aether for short, its posited existence dated back to the time of Aristotle, through Descartes leading to Maxwell and his 'Displacement' current. In 1887 Albert. A. Michelson, along with colleague Edward W. Morley, set out to prove, once and for all, the existence of the aether. For his work he won the Nobel Prize in 1907, the first American to do so, but remember, sometimes 'no' is the right answer.

Theory: Earlier in the 19th century Thomas Young had demonstrated wave interference with two slits and a columnated light source. Since light was thought to be a wave phenomena, Michelson proposed to use interference to pin down the aether. But how does interference work?

Interference occurs when two or more waves arrive at a particular point in space. It doesn't matter whether the waves are mechanical or electromagnetic in nature; all that matters is the instantateous amplitude of each wave at that point. (For practical purposes we shall consider only plane waves; therefore, the instantaneous amplitudes will termintate on a screen.) The extreme cases are when two waves are in phase and 180o out of phase:

In Phase Out of Phase
Figure 1A
Figure 1B
courtesy INDIANA UNIVERSITY

Notice when the waves are in phase they add to make a greater amplitude, and when they are out of phase their combined amplitude is zero. Therefore, on a screen that receives both in- and out of phase wave additions the result is a fringe pattern:

physics.las.umich.edu

Figure 2

where I is intensity (power/area). Notice the horizontal axis: d sin . This is how the phase difference is achieved, and it is called the path length difference (PLD). For a double slit experiment like Young's mentioned earlier, d sin important, but the Michelson interferometer achieves a PLD in a different way.

Examine the diagram below, courtesy Florida International University:

Figure 3

A beam of light from a laser travels to a beam splitter (a piece of glass with a reflective coating on the right face*); half of it is reflected and half transmitted. (Of course, Michelson and Morley didn't have a laser to work with, and when using polychromatic, incoherent light as they did, a lens and compensator** need to be added to the apparatus.) Half the beam travels a distance 2L1 and the other 2L2 from the BS to M1 and M2, respectively. If, after accounting for the thickness of the BS, one of these paths differs from the other, the pattern the screen will reveal that difference. Furthermore, if we change the position of M1even a little bit, the pattern of fringes will change accordingly. This allows for the measurement of extremely short distances, since the wavelength of visible light is on the order of 10-7m. And since we are using a column of laser light the fringe pattern will resemble a target's concentric circles.

The actual Michelson-Morley equipment looked like this:

courtesy UCSD

Figure 4

It was very heavy and floated on mercury to reduce vibration and for ease of turning. Why was ease of turning important? The two scientists figured that, as the Earth travels around the Sun, it moves through the aether similar to the current in a river. Therefore, if one beam is in the direction of motion but the other beam is perpendicular to it (radial from the Sun), there would be a light travel-time difference, and thereby the existence and qualities*** of the aether could be determined. Of course, orientation of the apparatus was critical!

Another cutting edge use of interferometry is the LIGO:

Figure 5

(See question 2)

So, did Michelson and Morely prove the existence of the luminiferous ether? Sometimes the right answer is no!

Task:

Equipment:

Figure 6

Figure 7

The following is from Pasco, the manufacturer:

Accurate Fringe Counting

Figure 8

The following techniques can help you make accurate measurements.

  1. It's not necessary that your interference pattern be perfectly symmetrical or sharp. As long as you can clearly distinguish the maxima and minima, you can make accurate measurements.
  2. It's easy to lose track when counting fringes. The following technique can help. Center the interference patter on the viewing screen using the thumbscrews on the back of the fixed mirror. Select a reference line on the millimeter scale and line it up with the boundary between a maximum and a minimum. Move the micrometer dial until the boundary between the next maximum and minimum reaches the same position as the original boundary. The fringe pattern should look the same as in the original position. One fringe has gone by.
  3. When turning the micrometer dial to count fringes, always turn it one complete revolution before you start counting, then continue turning it in the same direction while counting. This will almost entirely eliminate errors due to backlash in the micrometer movement. Backlash is a slight slippage that always occurs when you reverse the direction of motion in a mechanical system. (Turning the micrometer dial clockwise moves the movable mirror toward the right.)
  4. Always take several readings and average them for greater accuracy.
  5. The slip ring at the base of the micrometer knob adjusts the tension in the dial. Before making a measurement, be sure the tension is adjusted to give you the best possible control over the mirror movement.

Procedure:

  1. Align the laser and interferometer (Figure 6) so an interference pattern is clearly visible on your viewing screen.
  2. Adjust the micrometer knob (Figure 7) to a medium reading (approximately 50 µm). In this position, the relationship between the micrometer reading and the mirror movement is most nearly linear.
    1. As mentioned above, while using a laser the Compensator is not required.
  3. Turn the micrometer knob one full turn counterclockwise. Continue turning counterclockwise until the zero on the knob is aligned with the index mark. Record the micrometer reading.
    1. This is similar to the stand-alone micrometer you've used in Physics 201.
    2. When you reverse the direction in which you turn the micrometer knob, there is a small amount of give before the mirror begins to move. This is called mechanical backlash, and is present in all mechanical systems involving reversals in direction of movement. By beginning with a full counterclockwise turn, and then turning only counterclockwise when counting fringes, you can eliminate errors due to backlash.
  4. Adjust the position of the viewing screen so that one of the marks on the millimeter scale is aligned with one of the fringes in your interference pattern. You will find it easier to count the fringes if the reference mark is one or two fringes out from the center of the pattern.
  5. Rotate the micrometer knob slowly counterclockwise. Count the fringes as they pass your reference mark. Continue until some predetermined number of fringes have passed your mark (count at least 20 fringes). As you finish your count, the fringes should be in the same position with respect to your reference mark as they were when you started to count. Record the final reading of the micrometer dial.
  6. Record dm, the distance that the movable mirror moved toward the beam-splitter according to your readings of the micrometer knob. Remember, each small division on the micrometer knob corresponds to one µm (10-6 meters) of mirror movement.
  7. Record N, the number of fringe transitions that you counted.
  8. Repeat steps 3 through 7 ten times, recording your results each time.

Calculations:

You should set up a quick and dirty spreadsheet for these few calculations. For this lab, you don't need to turn in that file, just the .DOC with the spreadsheet table embedded.

Equation 1

Take the average of the ten calculations and state the wavelength of the HeNe laser with uncertainty.

Questions:

  1. In the discussion below Figure 4 we said that Michelson and Morley expected a light travel-time difference. Why? See University Physics, 13th ed., problem 3.34 for a hint.
  2. What is the LIGO and how does it work?

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*If you haven't yet learned in Physics 202, when a wave encounters an interface between two media there is always some reflection and some transmission. This characteristic is called impedence. Here we are assuming a 50-50 split.

**See how the purple ray going to Mirror 1 travels through the Beam Splitter twice but the red beam goes through only once? If we used something other than a laser we would need to account for the extra 'in the glass' distance with a compensator.

***Those qualities were thought to be zero density, since the aether appeared to have zero weight, zero viscosity, since the aether did not appear to affect planetary motion, but an infintely high bulk modulus in order to propogate light at its newly-confirmed extreme speed.