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<meta name="Author" content="C. L. Davis">
<title>Light and Optics - Multiple Slit Diffraction/Interference -
Diffraction Gratings - Physics 299</title>
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<h1><img src="ULPhys1.gif" height="50" align="texttop" width="189">
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<h1>Multiple Slit Diffraction/Interference - Diffraction Gratings<br>
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<font color="#ff0000"><i>"<span class="bqQuoteLink"></span></i></font><font
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Physics is actually too hard for physicists"</i></font><br>
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David Hilbert (Mathematician)<br>
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<ul>
<li> <big><b>IMPORTANT</b></big>: Don't be confused, diffraction
and interference are different aspects of the same phenomenon -
<b><i>the <a
href="http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves">superposition
of waves.</a></i></b></li>
</ul>
<blockquote>
<p><i><b>Interference:</b></i><b>&nbsp; Superposition of waves
from a finite number of "point" sources.<br>
</b></p>
<p><b><i>D</i><i>iffraction</i>:&nbsp;&nbsp; </b><b>Superposition
of waves from an infinite number of "point" sources,
comprising a single large source.<br>
</b></p>
</blockquote>
<img alt="fig1" src="lo_msdiffraction_fig1.jpg" height="296"
align="right" width="450">
<ul>
<li>Having discussed double slit interference/diffraction, the
natural extension is to 3, 4, 5...&nbsp; multiple slits.</li>
</ul>
<blockquote>
<p>The diagram at right illustrates a 5 slit configuration, where
the path difference at point P between waves from each of the
slits is dsin&#952; with a slit separation of "d".&nbsp; Clearly, if
the waves from all five slits are in phase, maximum intensity
will be observed at P when<br>
</p>
</blockquote>
<p align="center"> <img alt="eqn1" src="lo_interference_eqn1.jpg"
height="30" width="120"><br>
</p>
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<div align="left">where n = 0, 1, 2,...<br>
<br>
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<ul>
<li>A detailed mathematical analysis yields an intensity pattern
for N slits each of width d given by</li>
</ul>
<div align="center">&nbsp;<img alt="eqn1"
src="lo_msdiffraction_eqn1.jpg" height="63" width="189"><br>
<blockquote>
<div align="left">where &#946; is the same &#946; as in the single slit
diffraction and&nbsp; </div>
</blockquote>
</div>
</div>
<div align="center"><img alt="eqn2" src="lo_msdiffraction_eqn2.jpg"
height="69" width="133"><br>
<blockquote>
<div align="left">Note that this pattern is comprised of a
diffraction envelope together with the (sin<sup>2</sup>N&#947;)/sin<sup>2</sup>&#947;
term.&nbsp; This latter term leads to the existence of <i><b>principal
maxima</b></i> predicted by dsin&#952; = n&#955; together with much
weaker <i><b>secondary maxima</b></i> between the principal
maxima as shown below for a five slit example.<br>
<div align="center"><img alt="fig2"
src="lo_msdiffraction_fig2.jpg" height="334" width="498"><br>
<br>
<img alt="divider" src="divider_ornbarblu.gif" height="64"
width="100%"><br>
<h3><u><b>DIFFRACTION GRATINGS</b></u></h3>
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<ul>
<li>The <a
href="http://physics-animations.com/Physics/English/DG10/DG.htm">diffraction
grating</a> is an important experimental application
of the multiple slit maximum/minimum phenomenon.&nbsp;
In its simplest form a diffraction grating consistes of
a metal or glass plate with many very finely spaced
grooves or slits.</li>
</ul>
<ul>
<li>For a metal grating interference occurs in the
reflected light.&nbsp; For a glass grating reflected or
transmitted light will interfere.</li>
</ul>
<ul>
<li>The "slit" spacing, d,&nbsp; is typically defined by
the number of grooves per cm (or inch).</li>
</ul>
<ul>
<li>Principal maxima are located at angles &#952; given by sin&#952;
= n&#955;/d.&nbsp; Therefore, the smaller "d" (or the more
grooves per cm) the larger the angle &#952;.</li>
</ul>
<ul>
<li>By examining the exact intensity formula it can be
shown that the smaller "d" the brighter the principal
maxima are compared to the secondary maxima.</li>
</ul>
<ul>
<li>When an atom is "excited" the spectrum of light it
emits de-exciting back to its ground state is
characteristic of that&nbsp; particular atom.&nbsp;
Thus, observing the spectrum of light emitted by a star
gives an accurate measure of the elemental compostion of
the star.&nbsp; Since the angle &#952; depends on the
wavelength &#955; we can use a diffraction grating to obtain
the spectrum of the light emitted by the star.</li>
</ul>
<ul>
<li>For a "white" light source a diffraction grating may
lead to several "orders", corresponding to n = 1, 2,
3,... Each order will contain the complete spectrum of
colors (see below).<br>
</li>
</ul>
<div align="center"><img alt="fig3"
src="lo_msdiffraction_fig3.jpg" height="398" width="674"><br>
<blockquote>
<div align="left"><img alt="exclamation"
src="exclamation-icon.gif" height="30" width="31">
Depending on the value of "d" the various "orders" may
overlap.&nbsp; In other words red light (long
wavelength) in the first order (n=1) could have the
same value of &#952; as blue light (smaller wavelength) in
the second order (n=2).<br>
<br>
<img alt="exclamation" src="exclamation-icon.gif"
height="30" width="31"> Note that in a diffraction
grating red light is diffracted through a larger angle
than blue light, in contrast to the way in which a
prism separates the rainbow of colors (below).<br>
<div align="center"><img alt="fig4"
src="lo_msdiffraction_fig4.jpg" height="360"
width="480"><br>
</div>
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<blockquote> </blockquote>
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<blockquote> </blockquote>
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<center><i><font color="#ff0000">&nbsp; </font></i><i><font
color="#ff0000">
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charset=windows-1252">
A little boy refused to run anymore. When his mother asked him
why, he replied, "I heard that the faster you go, the shorter
you become</font></i><br>
<br>
<img src="celticbar.gif" height="22" width="576"> <br>
&nbsp;
<p><i>Dr. C. L. Davis</i><br>
<i>Physics Department</i><br>
<i>University of Louisville</i><br>
<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
<br>
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