235 lines
9.7 KiB
HTML
235 lines
9.7 KiB
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<!DOCTYPE html PUBLIC "-//w3c//dtd html 4.0 transitional//en">
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html;
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charset=windows-1252">
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<meta name="GENERATOR" content="Mozilla/4.7 [en] (X11; U; OSF1 V4.0
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alpha) [Netscape]">
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<meta name="Author" content="C. L. Davis">
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<title>Light and Optics - Multiple Slit Diffraction/Interference -
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Diffraction Gratings - Physics 299</title>
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</head>
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<body style="color: rgb(0, 0, 0); background-color: rgb(255, 255,
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255);" link="#0000ee" alink="#ff0000" vlink="#551a8b">
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<center>
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<h1><img src="ULPhys1.gif" height="50" align="texttop" width="189">
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</h1>
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</center>
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<center>
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<h1>Multiple Slit Diffraction/Interference - Diffraction Gratings<br>
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</h1>
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</center>
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<center><img src="celticbar.gif" height="22" width="576"> <br>
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<br>
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<font color="#ff0000"><i>"<span class="bqQuoteLink"></span></i></font><font
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color="#ff0000"><i> </i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font><font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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Physics is actually too hard for physicists"</i></font><br>
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<font color="#ff0000"><i><span class="bqQuoteLink">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</span></i></font> <font color="#ff0000"><i>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</i></font>
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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David Hilbert (Mathematician)<br>
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</center>
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<img src="netbar.gif" height="40" align="middle" width="100%">
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<blockquote>
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left">
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<div align="center">
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<div align="left"> </div>
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</div>
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</div>
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</div>
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</div>
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</div>
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</blockquote>
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<div align="center"> </div>
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<ul>
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<li> <big><b>IMPORTANT</b></big>: Don't be confused, diffraction
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and interference are different aspects of the same phenomenon -
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<b><i>the <a
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href="http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves">superposition
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of waves.</a></i></b></li>
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</ul>
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<blockquote>
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<p><i><b>Interference:</b></i><b> Superposition of waves
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from a finite number of "point" sources.<br>
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</b></p>
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<p><b><i>D</i><i>iffraction</i>: </b><b>Superposition
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of waves from an infinite number of "point" sources,
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comprising a single large source.<br>
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</b></p>
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</blockquote>
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<img alt="fig1" src="lo_msdiffraction_fig1.jpg" height="296"
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align="right" width="450">
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<ul>
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<li>Having discussed double slit interference/diffraction, the
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natural extension is to 3, 4, 5... multiple slits.</li>
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</ul>
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<blockquote>
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<p>The diagram at right illustrates a 5 slit configuration, where
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the path difference at point P between waves from each of the
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slits is dsinθ with a slit separation of "d". Clearly, if
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the waves from all five slits are in phase, maximum intensity
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will be observed at P when<br>
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</p>
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</blockquote>
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<p align="center"> <img alt="eqn1" src="lo_interference_eqn1.jpg"
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height="30" width="120"><br>
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</p>
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<blockquote>
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<div align="left">where n = 0, 1, 2,...<br>
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<br>
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</div>
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</blockquote>
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<div align="left">
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<ul>
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<li>A detailed mathematical analysis yields an intensity pattern
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for N slits each of width d given by</li>
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</ul>
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<div align="center"> <img alt="eqn1"
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src="lo_msdiffraction_eqn1.jpg" height="63" width="189"><br>
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<blockquote>
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<div align="left">where β is the same β as in the single slit
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diffraction and </div>
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</blockquote>
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</div>
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</div>
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<div align="center"><img alt="eqn2" src="lo_msdiffraction_eqn2.jpg"
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height="69" width="133"><br>
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<blockquote>
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<div align="left">Note that this pattern is comprised of a
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diffraction envelope together with the (sin<sup>2</sup>Nγ)/sin<sup>2</sup>γ
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term. This latter term leads to the existence of <i><b>principal
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maxima</b></i> predicted by dsinθ = nλ together with much
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weaker <i><b>secondary maxima</b></i> between the principal
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maxima as shown below for a five slit example.<br>
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<div align="center"><img alt="fig2"
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src="lo_msdiffraction_fig2.jpg" height="334" width="498"><br>
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<br>
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<img alt="divider" src="divider_ornbarblu.gif" height="64"
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width="100%"><br>
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<h3><u><b>DIFFRACTION GRATINGS</b></u></h3>
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</div>
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</div>
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</blockquote>
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<div align="left">
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<div align="center">
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<div align="left">
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<ul>
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<li>The <a
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href="http://physics-animations.com/Physics/English/DG10/DG.htm">diffraction
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grating</a> is an important experimental application
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of the multiple slit maximum/minimum phenomenon.
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In its simplest form a diffraction grating consistes of
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a metal or glass plate with many very finely spaced
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grooves or slits.</li>
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</ul>
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<ul>
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<li>For a metal grating interference occurs in the
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reflected light. For a glass grating reflected or
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transmitted light will interfere.</li>
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</ul>
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<ul>
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<li>The "slit" spacing, d, is typically defined by
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the number of grooves per cm (or inch).</li>
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</ul>
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<ul>
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<li>Principal maxima are located at angles θ given by sinθ
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= nλ/d. Therefore, the smaller "d" (or the more
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grooves per cm) the larger the angle θ.</li>
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</ul>
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<ul>
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<li>By examining the exact intensity formula it can be
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shown that the smaller "d" the brighter the principal
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maxima are compared to the secondary maxima.</li>
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</ul>
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<ul>
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<li>When an atom is "excited" the spectrum of light it
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emits de-exciting back to its ground state is
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characteristic of that particular atom.
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Thus, observing the spectrum of light emitted by a star
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gives an accurate measure of the elemental compostion of
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the star. Since the angle θ depends on the
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wavelength λ we can use a diffraction grating to obtain
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the spectrum of the light emitted by the star.</li>
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</ul>
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<ul>
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<li>For a "white" light source a diffraction grating may
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lead to several "orders", corresponding to n = 1, 2,
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3,... Each order will contain the complete spectrum of
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colors (see below).<br>
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</li>
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</ul>
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<div align="center"><img alt="fig3"
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src="lo_msdiffraction_fig3.jpg" height="398" width="674"><br>
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<blockquote>
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<div align="left"><img alt="exclamation"
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src="exclamation-icon.gif" height="30" width="31">
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Depending on the value of "d" the various "orders" may
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overlap. In other words red light (long
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wavelength) in the first order (n=1) could have the
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same value of θ as blue light (smaller wavelength) in
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the second order (n=2).<br>
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<br>
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<img alt="exclamation" src="exclamation-icon.gif"
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height="30" width="31"> Note that in a diffraction
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grating red light is diffracted through a larger angle
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than blue light, in contrast to the way in which a
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prism separates the rainbow of colors (below).<br>
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<div align="center"><img alt="fig4"
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src="lo_msdiffraction_fig4.jpg" height="360"
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width="480"><br>
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</div>
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</div>
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</blockquote>
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</div>
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</div>
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</div>
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</div>
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<blockquote> </blockquote>
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</div>
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<blockquote> </blockquote>
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<ul>
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</ul>
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<div align="center">
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<div align="left">
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<div align="center"> </div>
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</div>
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<img src="netbar.gif" height="40" width="100%"><br>
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</div>
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<br>
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<center><i><font color="#ff0000"> </font></i><i><font
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color="#ff0000">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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A little boy refused to run anymore. When his mother asked him
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why, he replied, "I heard that the faster you go, the shorter
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you become</font></i><br>
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<br>
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<img src="celticbar.gif" height="22" width="576"> <br>
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<p><i>Dr. C. L. Davis</i><br>
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<i>Physics Department</i><br>
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<i>University of Louisville</i><br>
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<i>email</i>: <a href="mailto:c.l.davis@louisville.edu">c.l.davis@louisville.edu</a>
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<br>
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</p>
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<p><img src="header-index.gif" height="51" width="92"> </p>
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</center>
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<p><br>
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</p>
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</body>
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</html>
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