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<h2 class="hd hd-2 unit-title">W15-PSP1: Diffraction Limited Microscope</h2>
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Microscope Resolution - part a
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We've just discussed the "Rayleigh criterion," which relates the diameter of an aperture, [mathjaxinline]D[/mathjaxinline], to the angle at which two objects are resolvable, [mathjaxinline]\Delta \theta[/mathjaxinline]&#8212;this angle subtends the first minimum of the Airy pattern from a point source. This criterion also depends on the wavelength of light that is observed. </p>
<table id="a0000000002" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
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<td class="equation" style="width:80%; border:none">[mathjax]\Delta \theta = 1.22 \dfrac {\lambda }{D}[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none">&#160;</td>
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<p>
All types of imaging systems are diffraction limited (*) including microscopes, which observe light that is reflected or emitted from micro and nanoscopic objects. The minimum resolvable size of a feature [mathjaxinline]d[/mathjaxinline], observed by a microscope with a "numerical aperture" [mathjaxinline]\mathrm{NA}[/mathjaxinline] is the following: </p>
<table id="a0000000003" class="equation" width="100%" cellspacing="0" cellpadding="7" style="table-layout:auto">
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<td class="equation" style="width:80%; border:none">[mathjax]d=\dfrac {\lambda }{2\mathrm{NA}}[/mathjax]</td>
<td class="eqnnum" style="width:20%; border:none">&#160;</td>
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<p>
where the "numerical aperture" is related to the effective angle of the light-collecting imaging system. </p>
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(*) <i class="itshape">There are some novel methods to overcome this limit in certain systems&#8212;more details can be found in the solution to Part (b).</i> </p>
<p><b class="bfseries">(Part a)</b> To observe smaller features using a microscope, which of the following should a scientist do? Select ALL that apply. </p>
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<text>a) observe shorter wavelengths of light</text>
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<text>b) observe longer wavelengths of light</text>
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<text>c) use a system with a smaller numerical aperture</text>
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<text>d) use a system with a larger numerical aperture</text>
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Microscope Resolution - part b
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<p><b class="bfseries">(Part b)</b> What is the smallest feature size that an optical microscope can resolve? Let the numerical aperture of the microscope be [mathjaxinline]\mathrm{NA}=1.4[/mathjaxinline] and the wavelength of light be [mathjaxinline]\lambda =500\, \mathrm{nm}[/mathjaxinline]. Express your answer as a number in units of nanometers. </p>
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<p style="display:inline">[mathjaxinline]d =[/mathjaxinline] </p>
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<p style="display:inline">[mathjaxinline]\mathrm{nm}[/mathjaxinline]</p>
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