Before beginning this lab you should read the section of your text about the Michelson Interferometer.  Your instructor will describe the techniques to set up the apparatus.  This must be done very carefully.  Once set up, it will work easily.

     There are two things we want to accomplish with the interferometer; measure the wavelength of light (in this case the laser) and secondly determine the effect of a gas in the line of sight.  These can both be accomplished readily if you read the text.

     Don't forget, this is relatively simple. You see one shift of a fringe line because the path length has changed by one full wavelength. That's what it boils down to. Good Luck!!!!!!

OBJECTIVES:

1.   To understand the operation and use of the Michelson Interferometer.

2.   To determine the wavelength of light with the Interferometer.

3.   To determine the refractive index of a gas and ultimately, the speed of light in the gas.

APPARATUS:

                  1 Michelson Interferometer Apparatus
                  1 Laser
                  1 Vacuum Pump

PROCEDURE:

1.  Read the sections of your text pertaining to this matter.

2.  Follow your instructor's guidance in setting up the apparatus.

3.  To calculate the wavelength of the light used (laser), merely count off 20 to 30 fringes and record the distance the micrometer dial moved.  One division of movement on the dial represents one micron of mirror movement.  (One revolution represents 25 microns of mirror movement).  If the mirror moves a distance d, the optical path has changed by a distance 2d since the light travels to the mirror and back.  Hence, divide 2d by the number of fringes to get the wavelength of light.

The correct value of the  l for this laser is 6328 A.  Find your % error.  Explain.

4.  For your information, the interferometer mirrors are flat to within 1/4 wavelength and are coated on one side for 80% reflectance and 20% transmission.

     The beam splitter is also flat to within 1/4 wavelength, and is coated for 50% transmission and 50% reflection.

     The moveable mirror is controlled by the micrometer dial on the base.  The uncertainty of movement is + 1%.  Each increment is one micron.  One total revolution is 25 microns of mirror movement.

5.  The condition for constructive interference is such that the path length difference must be an integral number of wavelengths of the light.  As the gas cell of length L is placed along one beam of the laser light:
 

If air is allowed to enter the chamber, then this is the same as changing the length of the optical path lengths which is:

Then we can say that  2 L (n-1)  = DL  (back and forth) or        n - 1 = DL / 2L
 

Thus, letting air into the chamber has the same effect as moving the mirror so that the effective difference in path length is 2DL .  Relating to  the number of fringes we can say:

Solve for the index of refraction of air from the above equations.
 

6.  Position the gas cell between the beam-splitter and the moveable mirror as described by your instructor.  Make minor adjustments to obtain a clear image.  Slowly pump the air out of the cell.  Count the number of fringes going by.  Note the final vacuum reading. l is the wavelength of light (you just measured it, but the true value for the laser is 6328 A), and L is the length of the gas cell, about 4 cm.

7.  Complete your writeup, including limitations, data analysis, summary, conclusions, and recommendations.