physics-class-12-unit-16-chapter-02-modern-physics-1-l-2-4-xulrbczfqwc

<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Polarization in Interference</B></Primary></p>
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<p><strong>Tunable Parameters</strong></p>
<ol>
<li>
<p>Distance between the screen and the slits</p>
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<p>Distance between the slits</p>
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<p>Wavelength of light</p>
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<p>Polarization of the two beams</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$<span style="color:blue">Polarization in Interference</span>$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electromagnetic Waves</B></Primary></p>
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<p><strong>Light</strong></p>
<p>$\left[\frac{1}{\sqrt{\mu_0 \epsilon_0}}\right]=L T^{-1}$</p>
<p>$ \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ = Speed of Light</p>
<p>$\epsilon_0$ = <strong>Permitting</strong></p>
<p>$\mu_0$ = <strong>Permeability</strong></p>
<p>$\mu_0$ = <strong>Definition</strong></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$<span style="color:blue">Electromagnetic Waves</span>$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electromagnetic Waves</B></Primary></p>
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<p>$\vec{E}(t, \vec{r}) \rightarrow$ Electric field</p>
<p>$\vec{B}(t, \vec{r}) \rightarrow$ Magnetic field</p>
<p>$\vec{B}(t, \vec{r})  \vec{E}(t) \vec{r}) k=\frac{2 \pi}{\lambda}$</p>
<p>$\omega = 2 \pi \nu$</p>
<p>$\nu \quad \vec{n} $</p>
<p>$\vec{E}$ = $\vec{E}_{0} \cos (k ~\vec{n}. \vec{r} - \omega t)$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/physics-class-12-unit-16-chapter-02-modern-physics-1-l-2_4-xulrbczfqwc-103.jpg"></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$<span style="color:blue">Electromagnetic Waves</span>$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electric Fields</B></Primary></p>
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<p>$ \vec{E_1}=\vec {E_{10}} \cos (k ~\hat{n}_1 \cdot \vec{r}-\omega t)$</p>
<p>$\vec{E_2}=\vec{E}_{20} \cos (k ~\hat{n}_2 \cdot \vec{r}-\omega t)$</p>
<p>$\hat{n}_1=\cos \alpha ~\hat{i}+\sin \alpha ~\hat{j}$</p>
<p>$\hat{n}_2=\cos \beta ~\hat{i}+\sin \beta ~\hat{j}$</p>
<p>$D \gg d$</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$<span style="color:blue">Electric Fields</span>$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electric Fields</B></Primary></p>
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<p>$\cos \alpha=\frac{D}{\left[\left(y-\frac{d}{2}\right)^2+D^2\right]^{1 / 2}}$</p>
<p>$\sin \alpha=\frac{y-\frac{d}{2}}{\left[\left(y-\frac{d}{2}\right)^2+D^2\right]^{1 / 2}}$=$\frac{y}{D}$</p>
<p>$\sin \alpha \approx \tan \alpha$</p>
<p>$\frac{d}{D} \gg 1$</p>
<p>$\approx$ 1 + binomial corrections</p>
<p>$ y + \frac{d}{2} \rightarrow \sin \beta $</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$<span style="color:blue">Electric Fields</span>$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electric Fields</B></Primary></p>
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<p>$\vec{E_1}=\vec{E_{10}} \cos [\vec{k} \cdot (\vec{r}-\frac{\vec{d}}{2})-\omega t]$</p>
<p>$\vec{E_2}=\vec{E_{20}} \cos [\vec{k} \cdot (\vec{r}+\frac{\vec{d}}{2})-\omega t]$</p>
<p>$ \vec{E_T}=\vec {E_1}+\vec{E_2}$</p>
<p>$\left|\vec{E}_ T\right|^2 \left|\vec{E}_ 1\right|^2+\left|\vec{E}_ 2\right|^2+ 2 {\vec{E}_ 1 \cdot \vec{E}_2}$</p>
<p>$D \gg d$</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$<span style="color:blue">Electric Fields</span>$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Electric Fields</B></Primary></p>
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<p>$\left\langle\cos ^2\right\rangle=\frac{1}{2}$</p>
<p>$\left\langle\vec{E^2_ {T}}\right\rangle = \frac{1}{2} \vec{E_ {10}^{2}} +\frac{1}{2} \vec{E_ {20}^2}+2\left\langle\vec{E_ 1} \cdot \vec{E_2}\right\rangle$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/physics-class-12-unit-16-chapter-02-modern-physics-1-l-2_4-xulrbczfqwc-321-2094.0.jpg"></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$<span style="color:blue">Electric Fields</span>$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Evaluation of the Cross Term</B></Primary></p>
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<p><strong>(Intereference Term)</strong></p>
<p>$\vec{E_1}=\vec{E_{10}} \cos[\vec{k} \cdot(\vec{r}-\frac{d}{2})-\omega t]$</p>
<p>$\vec{E_2}=\vec{E_{20}} \cos [\vec{k} \cdot (\vec{r}+\frac{\vec{d}}{2})-{\omega t}]$</p>
<p>$\langle\vec{E_ 1}. \vec{E_ 2}\rangle=\vec{E_ {10}} \cdot \vec{E_{20}}\langle \cos ()\cos ()\rangle$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/physics-class-12-unit-16-chapter-02-modern-physics-1-l-2_4-xulrbczfqwc-343-2260.8.jpg"></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$<span style="color:blue">Evaluation of the Cross Term</span>$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Evaluation of the Cross Term</B></Primary></p>
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<p>$\cos [\vec{k} \cdot (\vec{r}+\frac{\vec{d}}{2})-\omega t]$ $\cos [\vec{k} \cdot(\vec{r}-\frac{\vec{d}}{2})-\omega t]$</p>
<p>$\cos A \cos B =\frac{1}{2}[\cos (A-B)+\cos (A+B)]$</p>
<p>$\langle L H S\rangle=\left\langle\frac{1}{2}[\right. \cos 2(\vec{k} \cdot \vec{r}-\omega t)  +\cos \vec{k} \cdot \vec{d}]\rangle$</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$<span style="color:blue">Evaluation of the Cross Term</span>$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Evaluation of the Cross Term</B></Primary></p>
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<p>$\langle | \vec {E_ 1}|^2 + |\vec{E_ 2^2}|^2 + 2 \vec{E_ 1}.\vec{E_ 2}\rangle=\frac{1}{2} \vec{E_ {10}^2} + \frac{1}{2} \vec{E_ {20}^2}+ \frac{1\times 2}{2} \cos {(\vec k.\vec d)}\vec{E_ {10}}.\vec{E_{20}}$</p>
<p>$\vec{k} \cdot \vec{d}=k d \sin \alpha=k d\left(\frac{y}{D}\right)$</p>
<p>$ I(y)=\frac{1}{2}  \vec{E_{10}^2}+\frac{1}{2} \vec{E_{20}^2}+\vec{E_{10}} \cdot \vec{E_{20}}  \times \cos \left(k d \frac{y}{D}\right)$</p>
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<p><img alt="image" src="/subject-images/iitpal/image/physics-class-12-unit-16-chapter-02-modern-physics-1-l-2_4-xulrbczfqwc-409-2776.8.jpg"></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$<span style="color:blue">Evaluation of the Cross Term</span>$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Unpolarization</B></Primary></p>
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<p>$\vec{E_{10}} \cdot \vec{E_{20}}=\left|E_{10} ~E_{20}\right|$</p>
<p>Intensity will be a maximum if $ \cos () = -1$</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$<span style="color:blue">Unpolarization</span>$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Unpolarization</B></Primary></p>
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<p>$ \vec{E_{10}} \parallel \vec{E_{20}}$</p>
<p>$ \hat{E_{10}}=-\hat{E_{20}}$</p>
<p>$\vec{E_{10}} \cdot \vec{E_{20}}=0$</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$<span style="color:blue">Unpolarization</span>$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Intereference Conditions get Modified</B></Primary></p>
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<p>$ \vec{E_{10}} \parallel \vec{E_{20}}$ : Standard Conditions</p>
<p>$\vec{E_{10}}$ : Anti Parallel</p>
<p>$\vec{E_{20}}$ : Exactly Opposite Conditions</p>
<p>$\vec{E_{10}} \perp \vec{E_{20}}$: The Pattern Vanishes Completely</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$<span style="color:blue">Intereference Conditions get Modified</span>$\to$Interferometer$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Interferometer</B></Primary></p>
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<p><strong>Michaelson Interferometer</strong></p>
<p><strong>Max. Zehnder Interferometer</strong></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$<span style="color:blue">Interferometer</span>$\to$Polarization Effects$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
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<p><strong>Max Zehnder</strong></p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$<span style="color:blue">Polarization Effects</span>$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
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<p>AJP: Rodrigues</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$<span style="color:blue">Polarization Effects</span>$\to$Summary
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
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<h4 id="we-can-alter-the-conditions-for-maxima-and-minima-energy-is-proportional-to-vece2">We can alter the conditions for maxima and minima! Energy is proportional to $\vec{E^2}$</h4>
<p>Conclusion: Wave theory of light rests on secure experimental foundations</p>
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Photoelectric Effect$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$<span style="color:blue">Summary</span>
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<p><Success style="float:center;text-align:center;font-size:28px;" ><B>Modern Physics</B></Success></p>
<p><Primary style="float:center;text-align:center;font-size:24px;"><B>Photoelectric Effect</B></Primary></p>
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<p><strong>Time line</strong></p>
<table>
<thead>
<tr>
<th>Year</th>
<th>Discovery</th>
<th>Discover</th>
</tr>
</thead>
<tbody>
<tr>
<td>1887</td>
<td>Photoelectric emission</td>
<td>Hertz</td>
</tr>
<tr>
<td>1897</td>
<td>Electron</td>
<td>J J Thomson</td>
</tr>
<tr>
<td>1888 - 1902</td>
<td>Measurments</td>
<td>Hallawach and Lenard</td>
</tr>
<tr>
<td>1905</td>
<td>Theory</td>
<td>Einstien</td>
</tr>
<tr>
<td>1915</td>
<td>h</td>
<td>Millikan</td>
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<span style="color:blue">Photoelectric Effect</span>$\to$Two-Slit Experiment$\to$Polarization in Interference$\to$Electromagnetic Waves$\to$Electric Fields$\to$Evaluation of the Cross Term$\to$Play Around with Polarization$\to$Unpolarization$\to$Intereference Conditions get Modified$\to$Interferometer$\to$Polarization Effects$\to$Summary
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