To better understand the interferometer used by Michelson and Morley, we use a simplified version of their instrument to measure the wavelength of the laser light source used. The second part of the experiment consists in measuring the index of refraction of air by counting fringe shifts in the interference pattern. In the interferometer pictured below, the light from a (nearly) monochromatic source is split into two beams which recombine to form a visible pattern of areas of constructive and destructive interference; i.e. bright and dark fringes. When the effective length of one of the optical paths is changed by some means, then any given point on the interference pattern shifts from light to dark or vice-versa for each half-wavelength of path length change.
Your instructor will discuss the alignment of the interferometer using a laser. BE VERY CAREFUL WITH THE EQUIPMENT AS IT IS DELICATE AND EXPENSIVE! Never touch the mirror surfaces or bump, or drop any part of the apparatus. Consecutively, the movable mirror M2, the beam-splitter, the fixed mirror M1, and the lens holder with lens are aligned. A blank sheet of white paper taped to the cover of a book provides a viewing screen.
Whenever the laser is turned on, NEVER look directly into the beam or its reflection!
the laser light is given by:
Derive the above equation and calculate λ and compare to the specified value of 632.8 nm.
In this part of the experiment you are aiming to carefully control the vacuum within the air cell that you should place in the beam path in between the fixed mirror and the beam splitter. You can achieve a slow control of pressure in one of two ways.
In either approach the key is to pay careful attention to the movement of fringes so you need to make sure not to have the pressure change too quickly while you measure. One partner should count the number of fringe shifts as time goes by, and the other should record the pressure as a function of fringe-shift number. The relationship between the pressure change and the number of fringe shifts is given by (derive!):
where is the light wavelength, is the index of refraction of air at atmospheric pressure, is the length of the air cell, is the current atmospheric pressure, and , where is the air pressure inside the cell at the th fringe shift, and is the initial cell pressure. In the derivation of this expression one may assume that depends on as .
Plot versus on a graph and draw the best straight line through your data points. From the slope of this line and a knowledge of , , and determine . Estimate the experimental uncertainty on your measurements (by error propagation of various error sources) and compare to the literature value.