195 lines
7.7 KiB
HTML
195 lines
7.7 KiB
HTML
<!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 - Double Slit Diffraction/Interference -
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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>Double Slit Diffraction/Interference<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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All of physics is either impossible or trivial. It is
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impossible until you understand it, and then it becomes
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trivial.
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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<span></span><span class="bqQuoteLink"></span><span></span>"</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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Ernest Rutherford<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>Intensity pattern for single slit diffraction:</b></big></li>
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</ul>
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<div align="center"><img alt="eqn1" src="lo_ssdiffraction_eqn8.jpg"
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height="83" align="middle" width="134">
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where <img
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alt="eqn2" src="lo_ssdiffraction_eqn7.jpg" height="66"
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align="middle" width="129"><br>
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</div>
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<ul>
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</ul>
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<ul>
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<li><big><b>Intensity pattern for double slit interference:</b></big></li>
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</ul>
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<div align="center"><img alt="eqn1" src="lo_dsdiffraction_eqn1.jpg"
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height="37" align="middle" width="118">
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where
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<img alt="eqn4"
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src="lo_dsdiffraction_eqn4.jpg" height="59" align="middle"
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width="119"><br>
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<br>
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<blockquote>
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<div align="left">Note that φ' = φ/2, where φ is defined in the
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double slit interference analysis.<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>Remember that in the double slit interference analysis we
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(implicitly) assumed that the two slits were "point" wave
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sources. Of course in reality this is impossible, no
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sources are true "point" sources. An accurate
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description of double slit interference must include the
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effect of the finite width of each slit - that is, the
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diffraction phenomena from each slit. A detailed
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mathematical analysis leads to an intensity pattern at point
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P given by,</li>
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</ul>
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<div align="center"><img alt="eqn5"
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src="lo_dsdiffraction_eqn5.jpg" height="63" width="175"><br>
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<blockquote>
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<div align="left">Qualitatively, the interference pattern is
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modulated by the diffraction pattern, as indicated below.<br>
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<div align="center"><img alt="fig1"
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src="lo_dsdiffraction_fig1.gif" height="339"
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width="393"><br>
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</div>
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</div>
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</blockquote>
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<blockquote>
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<div align="left"><img alt="exclamatiom"
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src="exclamation-icon.gif" height="30" width="31"> Note
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that the slit width "a" must be smaller than the slit
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separation "d" (center to center).<br>
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</div>
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</blockquote>
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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"> The
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number of interference maximum underneath the central
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maximum of the diffraction envelope depends on the
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relative values of a and d.<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"> Diffraction minima occur at θ =
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λ/a , 2λ/a , 3λ/a... [ asinθ
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= nλ ]<br>
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Interference minima occur at θ = λ/2d , 3λ/2d ,
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5λ/2d... [ dsinθ = (n+1/2)λ ]<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>In the examples below the first intensity pattern
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has d = 3a, whereas the second pattern has d =
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(15/2)a<br>
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</li>
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</ul>
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</div>
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<blockquote>
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<div align="left"><br>
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<div align="center"><img alt="fig2"
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src="lo_dsdiffraction_fig2.jpg" height="231"
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width="489"> <img alt="fig3"
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src="lo_dsdiffraction_fig3.jpg" height="204"
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width="340"><br>
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</div>
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</div>
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</blockquote>
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<blockquote> </blockquote>
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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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<ul>
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</ul>
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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">
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<meta http-equiv="content-type" content="text/html;
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charset=windows-1252">
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</font></i><i><font 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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</font></i><i><font color="#ff0000">A year after almost failing
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her high school physics class, a girl told her older brother,
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<br>
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"You know, my physics teacher <i><b>was</b></i> right about
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the optical Doppler effect. You see those cars. The lights of
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the ones approaching us are white, but the lights of the ones
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moving away from us are red." </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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