... | ... | @@ -67,7 +67,7 @@ As shown in the above figure, under reflective polariscope, the circular polariz |
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```math
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E_{2} = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(kz-\omega t)}(-i\hat{f}+\hat{s}) = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(kz-\omega t)}e^{i\phi}(-i\hat{m_1}+\hat{m_2})
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```
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where $`I_0`$ is a constant as is called the background light intensity, $`k`$ is the wave number and $`\omega`$ is the frequency of the light, $`\hat{f}`$ and $`\hat{s}`$ is the fast and slow principle direction of the quarter-wave plate. Passing the specimen results in a $`\Delta = 2\phi(\sigma_1-\sigma_2)/f_{\sigma}`$ phase lead [5] to the $`\hat{m_1}`$ component of light. So in region (3):
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where $`I_0`$ is a constant as is called the background light intensity, $`k`$ is the wave number and $`\omega`$ is the frequency of the light, $`\hat{f}`$ and $`\hat{s}`$ is the fast and slow principle direction of the quarter-wave plate. Passing the specimen results in a $`\Delta = 2\pi(\sigma_1-\sigma_2)/f_{\sigma}`$ phase lead [5] to the $`\hat{m_1}`$ component of light. So in region (3):
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```math
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E_{3} = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(kz-\omega t)}e^{i\phi}(-ie^{-i\Delta}\hat{m_1}+\hat{m_2})
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```
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... | ... | @@ -77,7 +77,10 @@ E_{4} = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(-kz-\omega t)}e^{i\phi}(+ie^{-i\Delta}\ |
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```
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Passing the specimen again gives another $`\Delta`$ phase lead to the $`\hat{m_1}`$ light component. Therefore, in region (5):
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```math
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E_{5} = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(-kz-\omega t)}e^{i\phi}(+ie^{-2i\Delta}\hat{m_1}-\hat{m_2}) = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(-kz-\omega t)}e^{i\phi}[(ie^{-2i\Delta}cos\phi+sin\phi)\hat{f}+(ie^{-2i\Delta}sin\phi-cos\phi)\hat{s}]
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E_{5} = \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(-kz-\omega t)}e^{i\phi}(+ie^{-2i\Delta}\hat{m_1}-\hat{m_2})
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```
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```math
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= \frac{1}{\sqrt{2}}\sqrt{I_0}e^{i(-kz-\omega t)}e^{i\phi}[(ie^{-2i\Delta}cos\phi+sin\phi)\hat{f}+(ie^{-2i\Delta}sin\phi-cos\phi)\hat{s}]
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```
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Passing the quarter-wave plate again gives a $`-i`$ factor to the $`\hat{f}`$ component:
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```math
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... | ... | @@ -100,7 +103,7 @@ where the complex wave number $`\tilde{k} = k+i\kappa `$ and |
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k=\omega\sqrt{\frac{\epsilon \mu}{2}}[\sqrt{1+(\frac{\sigma}{\epsilon \omega})^2}+1]^{1/2};~
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\kappa =\omega\sqrt{\frac{\epsilon \mu}{2}}[\sqrt{1+(\frac{\sigma}{\epsilon \omega})^2}-1]^{1/2}
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```
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where $`\sigma`$ is the conductance of the conductor which connects the electric field $`\vec{E}`$ and the free current density: $`\vec{J}`$
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where $`\epsilon`$ is the electric permittivity, $`\mu`$ is the magnetic permeability, $`\sigma`$ is the conductance of the conductor which connects the electric field $`\vec{E}`$ and the free current density: $`\vec{J}`$
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```math
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\vec{J}_f=\sigma \vec{E}
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```
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