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\subsubsection*{PHSX 222L\hfill Interference and Diffraction\hfill Name:\underline{\hspace*{2in}}}


\underline{Object:} To use a two-slit interference pattern to measure 
the wavelength of laser light and then use the laser to determine the 
line spacing of a grating, and to observe a one-slit diffraction 
pattern and a two-dimensional diffraction pattern.

\underline{Theory:} Whether light is a wave or particles was one of
the great debates in the history of physics.  One of the experiments
that convincingly demonstrated the wave nature of light was the
two-slit experiment performed by Thomas Young.  Two close narrow
parallel slits $d$ apart (measured from center to center) serve as a
pair of coherent light sources when illuminated by a monochromatic
light source such as a laser or the light that emerges from a previous
single slit.  They produce a pattern of alternating light and dark
bands on a screen a distance $L$ away from the slits.  
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A bright spot
(constructive interference) is seen on the screen when the path length
difference between the two slits is an integral multiple of the
wavelength $\lambda$; and a dark spot (destructive interference) is
seen when the path length difference is an odd multiple of $\lambda
/2$.  If $y$ is the distance on the screen away from the central
maximum and we assume that $L \gg d$ and $d \gg \lambda$ (see
discussion on pp.~1187-1190 and figure 37.13 in Serway) then
\begin{equation}\label{bright}
y_{\rm bright} \approx {\lambda L\over d} m 
\ \ \ \ \ \ \ \ \ \ \ \ \ m = (0, \pm 1, \pm 2, \ldots)
\end{equation}
where $m$ is called the order number, and
\begin{equation}
y_{\rm dark} \approx {\lambda L\over d} \left (m+\frac{1}{2}\right )
\ \ \ \ \ \ \ \ \ \ \ \ \ m = (0, \pm 1, \pm 2, \ldots).
\end{equation}

If instead of just two slits we use a grating consisting of a very
large number of extremely narrow slits separated by very small
distances, we can obtain an interference pattern (see section 38.4 in
Serway) in which the lines corresponding to different wavelengths are
distinctly spaced.  (In fact, modern optical spectrometers almost
always use diffraction gratings rather than prisms to obtain spectra
of light with many wavelengths present.)  However, in this experiment
we will use the value of $\lambda$ just obtained for the two-slit
experiment for monochromatic light to determine the line spacing $d$
of a diffraction grating.

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For single slit of width $a$, we also observe a diffraction pattern of 
alternating light and dark spots or bands because light from 
one part of the slit interferes with light from another part of the 
slit.  See section 38.2 in Serway, especially figure 38.11.  
However, the equation is now for dark spots:
\begin{equation}\label{single}
y_{\rm dark} \approx {\lambda L\over a} m 
\ \ \ \ \ \ \ \ \ \ \ \ \ m = (\pm 1, \pm 2, \ldots).
\end{equation}
Compare with equation 38.1 in Serway and note the appropriate 
approximations that must be made.

\underline{Safety Considerations:} Never intentionally shine a laser 
in anyone's eye, and take precautions that the beam doesn't go in 
yours either.  Please handle the slit patterns carefully as they are 
fragile (made from 0.005 mm electroformed nickel) and expensive.

\underline{Apparatus:}  Draw a detailed diagram of the 
equipment set-up.

\underline{Procedure:} 
\vspace{-.25in}
\begin{enumerate}

	
\item\label{one} In equation \ref{bright} $L$ is easily varied (but if it is too 
small the approximations may not hold well), and so is $d$ (by 
using different sets of slits); different values of $m$ are also 
easily observed.  With a Helium-Neon laser illuminating a double slit, 
take data for $y_{\rm bright}$ (you might want to average data on both 
sides of the center, {\em i.e.}, both the positive and negative values 
of $m$) for various combinations of these variables.

\item\label{two} Plot $y_{\rm bright}$ vs.  ${L\over d }m$ and compare your slope
to the accepted value for $\lambda$ (632.8 nm for red HeNe lasers and
543 nm for green HeNe lasers).
 
\item Repeat for a multiple slit pattern (3 or 4 or 5 slits).

\item Replace the multiple slit with the diffraction grating and again 
measure $y_{\rm bright}$ on both sides of the central maximum.  

\item Use the accepted value for $\lambda$ and compute $d$ from equation
\ref{bright} and invert it to get $n$ (the line density of the
grating) and compare with the value stated on the grating.

\item Repeat procedures \ref{one} and \ref{two} for a two-dimensional pattern. 

\item Perform a similar procedure for single-slit diffraction and for
a circular aperture.

\end{enumerate}


\goodbreak
\vspace{-.15in}
\underline{Questions:} 
\vspace{-.25in}
\begin{enumerate}
\item For more precise measurements, the above approximations should 
not be used.  How much do they contribute to your error?  What is the 
more accurate version of the formula?

\item In this laboratory you observed both interference and 
diffraction.  What is the difference between them?

\item What difference do you see in the interference pattern for green 
laser vs. red laser, and why?

\item In crystals, atoms are arranged in periodic structures that can
be thought of as diffraction gratings with a very large line density. 
What type of electromagnetic radiation should be used in such
experiments?  Why?  (Hint: see section 38.5 in Serway.)  (The
structure of DNA was discovered this way; you may want to read {\em
The Double Helix}.)

\end{enumerate}

\vspace{-.15in}
\underline{Conclusions:} 


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