pHYSICS

Experiment 4

Michelson Interferometer:

The Michelson interferometer is the best example of what is called an amplitude-splitting interferometer. It was invented in1893 by Albert Michelson, to measure a standard meter in units of the wavelength of the red line of the cadmium spectrum. With an optical interferometer, one can measure distances directly in terms of wavelength of light used, by counting the interference fringes that move when one or the other of two mirrors are moved. In the Michelson interferometer, coherent beams are obtained by splitting a beam of light that originates from a single source with a partially reflecting mirror called a beam splitter. The resulting reflected and transmitted waves are then re-directed by ordinary mirrors to a screen where they superimpose to create fringes. This is known as interference by division of amplitude. This interferometer, used in 1817 in the famous Michelson- Morley experiment, demonstrated the non-existence of an electromagnetic-wave-carrying ether, thus paving the way for the Special theory of Relativity.

A simplified diagram of a Michelson interferometer is shown in the fig: 1.

Light from a monochromatic source S is divided by a beam splitter (BS), which is oriented at an angle 45° to the beam, producing two beams of equal intensity. The transmitted beam (T) travels to mirror M₁ and it is reflected back to BS. 50% of the returning beam is then reflected by the beam splitter and strikes the screen, E. The reflected beam (R) travels to mirror M₂, where it is reflected. 50% of this beam passes straight through beam splitter and reaches the screen.

Since the reflecting surface of the beam splitter BS is the surface on the lower right, the light ray starting from the source S and undergoing reflection at the mirror M₂ passes through the beam splitter three times, while the ray reflected at M₁ travels through BS only once. The optical path length through the glass plate depends on its index of refraction, which causes an optical path difference between the two beams. To compensate for this, a glass plate CP of the same thickness and index of refraction as that of BS is introduced between M₁ and BS. The recombined beams interfere and produce fringes at the screen E. The relative phase of the two beams determines whether the interference will be constructive or destructive. By adjusting the inclination of M₁ and M₂, one can produce circular fringes, straight-line fringes, or curved fringes. This lab uses circular fringes

Measurement of wavelength:

Using the Michelson interferometer, the wavelength of light from a monochromatic source can be determined. If M₁ is moved forward or backward, circular fringes appear or disappear at the centre. The mirror is moved through a known distance d and the number N of fringes appearing or disappearing at the centre is counted. For one fringe to appear or disappear, the mirror must be moved through a distance of λ/2. Knowing this, we can write,

Materials required

Laser light source, Michelson interferometer kit, optical bench, meter scale.

Procedure

Procedure for performing the real lab:

To find the wavelength of the laser source:

• The laser beam must strike at the center of the movable mirror and should be reflected directly back into the laser aperture.

• Adjust the position of the beam splitter so that the beam is reflected to the fixed mirror.

• Adjust the angle of beam splitter to be 45 degrees. There will be two sets of bright spots on the screen, one set from the fixed mirror and another from the movable mirror.

• Adjust the angle of the beam splitter to make the two sets of spots as close together as possible.

• With the screws on the back of the adjustable mirror, adjust the mirror’s tilt until the two sets of spots on the screen coincide.

• Expand the laser beam slowly by rotating the collimating lens in front of the laser.

• Align the laser with the interferometer and make certain that the fringes are moving when the micrometer screw is turned.

• Mark a point on the screen and note the micrometer reading.

• As the screw is moved, the fringes begin to displace. Count the number of fringes N that move past the mark (either inward or outward). To avoid the effects of backlash in the micrometer screw, turn the micrometer handle one full turn before starting the count.

• Note the micrometer readings at the beginning and end of the count. Calculate the distance d' the mirror is moved, according to the beginning and ending micrometer readings. Repeat the procedure several times. Average the readings.

• With a known wavelength laser, use d = Nλ/2 to calculate the actual distance moved. The calibration constant of the interferometer is then k= d/d'. All subsequent distance measurements with the micrometer should be multiplied by the calibration constant k. Ideally, k would be exactly 1, but factors such as wear and thermal expansion can cause it to vary.

• Once the calibration constant is known, if the laser source has an unknown wavelength, it can be calculated with the same equation.

Observations and calculations:

Least Count = ..... cm

Calibration constant of the apparatus= .....

No: of fringes, N =.....

Distance moved for N fringes, d =...... cm.

Then,

Observation Table

Result

The wavelength of the given laser source = .......... nm.

Reference Material

1. Thermal Physics, S. Garg, R. Bansal and C. Ghosh, 1993, Tata McGraw-Hill

2. Virtual Lab (https://vlab.amrita.edu/index.php?sub=1&brch=194&sim=354&cnt=1)

Questions

1.What is interference?

2.What is path difference?

3.How a beam splitter works?