http://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&feed=atom&action=historyBeer's Law and Beyond - Revision history2024-03-28T11:05:01ZRevision history for this page on the wikiMediaWiki 1.27.1http://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=2879&oldid=prevAdmin at 20:06, 29 September 20172017-09-29T20:06:47Z<p></p>
<a href="http://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=2879&oldid=2841">Show changes</a>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=2841&oldid=prevAdmin: Replaced content with "<span style="font-family:Georgia;">Keith B. Oldham and J. Mark Parnis <span style="font-family:Georgia;">Chemical Properties Research Group, Department of Chemist..."2017-09-20T11:11:13Z<p>Replaced content with "<span style="font-family:Georgia;"><a href="http://www.lumipedia.org/index.php?title=Keith_B._Oldham&action=edit&redlink=1" class="new" title="Keith B. Oldham (page does not exist)">Keith B. Oldham</a> and <a href="http://www.lumipedia.org/index.php?title=J._Mark_Parnis&action=edit&redlink=1" class="new" title="J. Mark Parnis (page does not exist)">J. Mark Parnis</a> <span style="font-family:Georgia;">Chemical Properties Research Group, Department of Chemist..."</p>
<a href="http://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=2841&oldid=1105">Show changes</a>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1105&oldid=prevAdmin at 05:51, 16 February 20172017-02-16T05:51:27Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 05:51, 16 February 2017</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline"><chem>H2O</chem></del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td></tr>
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</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1104&oldid=prevAdmin at 05:50, 16 February 20172017-02-16T05:50:51Z<p></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 05:50, 16 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13" >Line 13:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]  </div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]  </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline"><chem>H2O</chem></ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1055&oldid=prevAdmin: /* 3. The bivariate Beer laws */2017-02-15T21:48:12Z<p><span dir="auto"><span class="autocomment">3. The bivariate Beer laws</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 21:48, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l110" >Line 110:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}\tag {11}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}\tag {11}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\begin{Bmatrix}</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">B_{0}(z)=1\\ </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">B_{1}(z)=z-1\\ </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">B_{2}(z)=2z^2-3z+1\\</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">etc.\\ </del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\end{Bmatrix} andgenerally B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}</del></div></td><td colspan="2"> </td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">The recursion relationship <math> B_{k+1}(z)=[z-1]d(zB_{k} (z))/dz</math> applies but, for computer implementation, the recurrence of the coefficients,</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">The recursion relationship <math> B_{k+1}(z)=[z-1]d(zB_{k} (z))/dz</math> applies but, for computer implementation, the recurrence of the coefficients,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1054&oldid=prevAdmin: /* 3. The bivariate Beer laws */2017-02-15T21:47:35Z<p><span dir="auto"><span class="autocomment">3. The bivariate Beer laws</span></span></p>
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<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 21:47, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l110" >Line 110:</td>
<td colspan="2" class="diff-lineno">Line 110:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}\tag {11}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}\tag {11}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\begin{Bmatrix}</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">B_{0}(z)=1\\ </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">B_{1}(z)=z-1\\ </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">B_{2}(z)=2z^2-3z+1\\</ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">etc.\\ </ins></div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\end{Bmatrix} andgenerally B_{k}(z)=\sum_{h=0}^{k}b_{k, h}z^{k}</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">The recursion relationship <math> B_{k+1}(z)=[z-1]d(zB_{k} (z))/dz</math> applies but, for computer implementation, the recurrence of the coefficients,</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">The recursion relationship <math> B_{k+1}(z)=[z-1]d(zB_{k} (z))/dz</math> applies but, for computer implementation, the recurrence of the coefficients,</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1053&oldid=prevAdmin: /* 1. The classical law and its history */2017-02-15T21:24:35Z<p><span dir="auto"><span class="autocomment">1. The classical law and its history</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class='diff-marker' />
<col class='diff-content' />
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 21:24, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l33" >Line 33:</td>
<td colspan="2" class="diff-lineno">Line 33:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\log_{10}\frac{I(0)}{I(L)}=\varepsilon c L\tag {3}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\log_{10}\frac{I(0)}{I(L)}=\varepsilon c L\tag {3}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">ln</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">Citing the earlier findings [1] of [[Pierre Bouguer]], the 1760 treatise [2] of [[Johann Lambert]] publicized the linear dependence of the logarithm of the <math>I(0)/I(L)</math> ratio on <math>L</math>, whereas its analogous dependence on <math>c</math> remained unrecognized until the work [3] of [[August Beer]] almost a century later. Equation (3) is the form in which '''Beer’s law''' (also known as the Beer-Lambert or Beer-Lambert-Bouguer law) is most commonly encountered.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">Citing the earlier findings [1] of [[Pierre Bouguer]], the 1760 treatise [2] of [[Johann Lambert]] publicized the linear dependence of the logarithm of the <math>I(0)/I(L)</math> ratio on <math>L</math>, whereas its analogous dependence on <math>c</math> remained unrecognized until the work [3] of [[August Beer]] almost a century later. Equation (3) is the form in which '''Beer’s law''' (also known as the Beer-Lambert or Beer-Lambert-Bouguer law) is most commonly encountered.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1052&oldid=prevAdmin: /* 1. The classical law and its history */2017-02-15T21:24:06Z<p><span dir="auto"><span class="autocomment">1. The classical law and its history</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class='diff-marker' />
<col class='diff-content' />
<col class='diff-marker' />
<col class='diff-content' />
<tr style='vertical-align: top;' lang='en'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 21:24, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l33" >Line 33:</td>
<td colspan="2" class="diff-lineno">Line 33:</td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\log_{10}\frac{I(0)}{I(L)}=\varepsilon c L\tag {3}</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>\log_{10}\frac{I(0)}{I(L)}=\varepsilon c L\tag {3}</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div></math></div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div> </div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">ln</ins></div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">Citing the earlier findings [1] of [[Pierre Bouguer]], the 1760 treatise [2] of [[Johann Lambert]] publicized the linear dependence of the logarithm of the <math>I(0)/I(L)</math> ratio on <math>L</math>, whereas its analogous dependence on <math>c</math> remained unrecognized until the work [3] of [[August Beer]] almost a century later. Equation (3) is the form in which '''Beer’s law''' (also known as the Beer-Lambert or Beer-Lambert-Bouguer law) is most commonly encountered.</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">Citing the earlier findings [1] of [[Pierre Bouguer]], the 1760 treatise [2] of [[Johann Lambert]] publicized the linear dependence of the logarithm of the <math>I(0)/I(L)</math> ratio on <math>L</math>, whereas its analogous dependence on <math>c</math> remained unrecognized until the work [3] of [[August Beer]] almost a century later. Equation (3) is the form in which '''Beer’s law''' (also known as the Beer-Lambert or Beer-Lambert-Bouguer law) is most commonly encountered.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1044&oldid=prevAdmin: /* 1. The classical law and its history */2017-02-15T20:49:27Z<p><span dir="auto"><span class="autocomment">1. The classical law and its history</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
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<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:49, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]] When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]  </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td colspan="2"> </td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
</table>Adminhttp://www.lumipedia.org/index.php?title=Beer%27s_Law_and_Beyond&diff=1043&oldid=prevAdmin: /* 1. The classical law and its history */2017-02-15T20:49:07Z<p><span dir="auto"><span class="autocomment">1. The classical law and its history</span></span></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<col class='diff-marker' />
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<tr style='vertical-align: top;' lang='en'>
<td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 20:49, 15 February 2017</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l12" >Line 12:</td>
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<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>== 1. The classical law and its history ==</div></td></tr>
<tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;"> <del class="diffchange diffchange-inline">When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium </del>[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]]that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><span style="font-family:Georgia;">[[File:Fig.1.jpg|thumb|300px|Figure 1.|Figure 1. Beer’s law describes the diminution in intensity of a beam of light as it traverses a medium that contains an absorber, as suggested by the decreasing number of arrows.]] <ins class="diffchange diffchange-inline">When electromagnetic radiation, such as ultraviolet or visible light, passes through a transparent medium </ins>that contains an absorber of that illumination, the radiation’s intensity diminishes steadily with passage through the medium.  Commonly the radiation is in the form of a collimated beam that impinges perpendicularly on a slab of width <math>L</math> of the medium, as suggested diagrammatically in Figure 1. <span style="font-family:Georgia;">One may conjecture that, at any illuminated plane <math>x</math> within the medium, the decrease in the intensity <math>I</math> of the radiation with distance would be proportional to the uniform concentration <math>c</math> of the absorber and to the local intensity of the light at that point; that is</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr>
<tr><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td><td class='diff-marker'> </td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div><math></div></td></tr>
</table>Admin