Determination of the wavelengths of the Sodium doublet lines and the measurement of the thickness of a thin transparent film using a Michelson interferometer

My report on the Michelson interferometer experiment for the lab course during the second year of my MSci. Might be of use to anyone taking the second year lab course but, otherwise, not terribly exciting.

Authors:

Luke Pomfrey

Abstract:

This experiment aims to discern the wavelengths of the two sodium doublet lines by the use of a Michelson-interferometer, and then to discern the thickness of a sample of Mylar film utilising the same equipment.

The following values for the wavelength of the sodium doublet lines were calculated:

 \begin{equation*}
  \begin{aligned}
   \lambda_{1} &= \left( 589.01 \pm 0.01 \right) \times 10^{-9} \textrm{ m} \\
   \lambda_{2} &= \left( 589.59 \pm 0.01 \right) \times 10^{-9} \textrm{ m}
  \end{aligned}
 \end{equation*}

These values are remarkably close to the accepted values for the two sodium D-lines of:

 \begin{equation*}
  \begin{aligned}
   \lambda_{A1} &= 588.99  \times 10^{-9} \textrm{ m} \\
   \lambda_{A2} &= 589.59  \times 10^{-9} \textrm{ m}
  \end{aligned}
 \end{equation*}

The thickness of the Mylar film was found to be:

 \begin{equation*}
  t = \left( 1.66 \pm 0.06 \right) \times 10^{-5} \textrm{ m}
 \end{equation*}

Which is to the same order as the manufacturer specified thickness of the Mylar of:

\begin{equation*}
 (1.3 \pm 0.1) \times 10^{-5} \textrm{ m}
\end{equation*}

This experiment could be considered a success. There are, however, a number of improvements which could be made to improve the rather large level of human error involved in the procedures performed.

Cite:

L. Pomfrey. Determination of the wavelengths of the Sodium doublet lines and the measurement of the thickness of a thin transparent film using a Michelson interferometer. March, 2007.