Using a Michelson Interferometer to Find the Index of Refraction of Materials

EE4441

1.0Introduction

1.1Purpose

This experiment focuses on the way an index of refraction can be found by using a laser. Several aspects of interference, materials, magnification, and propagation are uncovered. Through this experiment, one should discover not only how the index of refraction of any transparent material is found with a laser, but why it is possible.

1.2Background

The Michelson Interferometer was invented in 1881 by an American physicist named Albert Abraham Michelson. He invented it to be used in the Michelson-Morley experiment to conduct tests concerning the speed of light. However, this application can be used in many other locations other than for finding the speed of light.

One excellent aspect of the Michelson Interferometer is that it causes interference usually by the superposition of two plane waves. When two waves of identical magnitude and unequal phases are superimposed, a fringe pattern occurs. This fringe pattern is the result of constructive and destructive interference. Equation 1.1 shows mathematically how the two waves are combined, where is the intensity and is the phase of the wave.

(1.1)

Interference is considered constructive if the amplitude of the wave has been magnified or is larger than its original intensity. The intensity is maximized at four times its original value of , which is also known as complete constructive interference. This occurs when the delay distance from the trailing wave to the original wave is an integer multiple of its wavelength .

Interference is considered destructive if the amplitude of the wave is zero or smaller than its original value. Complete destructive interference occurs when the delay distance from the trailing wave to the original wave is an odd integer multiple of its wavelength divided by two .

2.0Setup

2.1Parts

This is the list of parts required for the experiment.

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  • 1 HeNe 632.8nm Laser
  • Laser Mount
  • Optical Breadboard
  • 1 Half-Silver Mirror
  • 5 Post Mounts
  • 7 Optical Post Holders
  • 7 Steel Posts
  • 3 Lens Holders
  • 2 Mirror Mounts
  • 1 Micrometer Stage
  • 1 360˚ Rotatable Stage
  • 1 Beam Splitter Stage
  • 2 Highly Reflective Mirrors
  • 1 Target Holder
  • 3 Lenses
  • 2 Materials to Test
  • Box of Screws
  • Designated Allen Wrenches
  • Cleaning Wipes (as needed)

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2.2Layout

Figure 2.1 shows a top view layout for this experiment.

Figure 2.1 – Layout

2.3Assembly

The steps provided in this section must be done sequentially as the results of the experiment may be inaccurate.

2.3.1Mount the laser to the optical board exactly in the center of the board to one side so that as much room as possible is given to the setup.

2.3.2Plug in and turn on the laser to allow for warm-up.

2.3.2.1Do not look directly into the laser!

2.3.3Place a post holder on each stage listed in section 2.1 except for the beam splitter stage.

2.3.4Place a steel post in each of the post holders in 2.3.1.

2.3.5Carefully secure both mirrors into their select mounts.

2.3.5.1A piece of paper behind the mirror helps keep it secure.

2.3.6Place and secure the three lens holders, one mirror, and the beam splitter stage on five fixed stages.

2.3.6.1Do not secure them to the optical board at this time.

2.3.7Place and secure the target holder on the rotatable stage assembly.

2.3.8Place and secure the other mirror to the moveable micrometer stage.

2.3.9Place and secure the fixed mirror assembly directly across from the laser as far to the edge as the holes will allow.

2.3.10Adjust the mirror so the beam is reflected back into the laser cavity.

2.3.11Place and secure one of the lens assemblies approximately 2 inches in front of the laser.

2.3.12Carefully place the desired lens into the assembly and adjust so that the beam again reflects into the laser cavity.

2.3.13Place and secure the beam splitter stage assembly in the center of the board.

2.3.14Carefully secure the half-silver mirror on the stage.

2.3.14.1Ensure that the front edge is perpendicular to the laser beam.

2.3.15Place and secure the movable mirror assembly in the center of the left side so that the laser beam is incident on it from the beam splitter.

2.3.15.1Note that the distances from mirrors to the beam splitter must be different.

2.3.16Place and secure the rotatable target assembly between the movable mirror and the beam splitter.

2.3.17Place and secure the two lens assemblies between the beam splitter and the desired image screen (i.e. piece of paper).

2.3.18Carefully secure the 2 lenses into their assemblies and adjust so that the beam from the movable mirror is directly in the center of each.

2.3.19Two beams should be visible at this point on the screen.

2.3.20Adjust the movable mirror (not its stage) until the two beams combine.

2.3.21The combined image should reflect the one shown in Figure 2.2.

Figure 2.2 – Fringe Pattern

3.0Procedure

3.1Material Orientation

Place the desired first material into the target holder. Ensure that it is pressed up into the holder so that there is no more than a 90˚ angle between it and the optical board. Set the rotation stage initially to zero and position the material so that it is perpendicular to the beam. The material is perfectly perpendicular if the fringe pattern does not change with small increments from zero (less than one degree). Secure the post in its holder.

3.2Counting Fringes

Depending on what way that the material is rotated, fringes will appear or disappear. It is recommended to start at the desired displacement and rotate back to zero. It makes things much easier when counting. The more displacement on the material, the faster the fringes move.

Rotate the stage slowly towards zero. Count every fringe that disappears in the center of the screen (do not count outer fringes). As the stage is nearing zero, fringe movement will decrease significantly, until it eventually stops all together. Record the number of fringes that were counted up to this point.

3.3Determining the Index of Refraction

Once the fringes have been counted, one can effectively compute the index of refraction with the following equation,

(3.1)

where is the laser wavelength, M is the number fringes, is the displacement, and is the thickness of the material. Be careful when using this equation and use correct units. Is used in degrees or radians? Record your findings in section 5.

3.4Repeat

Repeat this procedure for the second material.

4.0Considerations

4.1Why does the number of fringes increase as the material is rotated?

4.2What could be expected if a thicker sample of the same materials were used in this experiment?

4.3Why was the beam not redirected back into the laser cavity once the beam splitter was placed into the setup?

4.4Why would it be more difficult to find the index of refraction of optical calcite?

4.5Could this setup be used to find the index of refraction of air? If so, how?

4.6Why do the fringes move as the material is rotated?

4.7Why do the mirrors need to be different lengths away from the beam splitter?

4.8If unknown, could the wavelength a laser be found with this setup? How?

4.9What would happen if a polarization beam splitter was used instead of a half-silver mirror? How could this be corrected?

5.0Data Sign Off Sheet

Name(s):

Material 1 – Polycarbonate

Thickness: 3/32 inches

Displacement / 10˚ / 15˚
Modes
Index of Refraction

Material 2 – Microscope Slide

Thickness: 1mm

Displacement / 10˚ / 15˚
Modes
Index of Refraction

Signature: ______

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