Polarization of Light

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  • Degree of polarization of light: $$P=\frac{I_{max}-I_{min}}{I_{max}+I_{min}}.$$
  • Malus's law: $$I = I_0 \cos^2\phi.$$
  • Brewster's law: $$\tan \theta_B = n_2/n_1.$$
  • Fresnel equations for intensity of light reflected at the boundary between two dielectrics: $$I^\prime_\bot = I_\bot\frac{\sin^2(\theta_1-\theta_2)}{\sin^2(\theta_1+\theta_2)}, I^\prime_\parallel = I_\parallel\frac{\tan^2(\theta_1-\theta_2)}{\tan^2(\theta_1+\theta_2)},$$ where $I_\bot$ and $I_\parallel$ are the intensities of incident light whose electric vector oscillations are respectively perpendicular and parallel to the plane of incidence.
  • A crystalline plate between two polarizers $P$ and $P^\prime$. If the angle between the plane of polarizer $P$ and the optical axis $OO^]prime$ of the plate is equal to $45^\text{o}$, the intensity $I^\prime$ of light which passes throught the polarizer $P^\prime$ turns out to be either maximum or minimum under the following conditions:
    Polarizers $P$ and $P^\prime$ $\delta=2\pi k$ $\delta=(2k+1)\pi$
    parallel $I^\prime_\parallel = \text{max}$ $I^\prime_\parallel = \text{min}$
    crossed $I^\prime_\bot = \text{min}$ $I^\prime_\bot = \text{max}$
    Here $\delta = 2\pi(n_0-n_e)d/\lambda$ is the phase difference between the ordinary and extraordinary rays, $k=0,1,2,...$
  • Matural and magnetic rotation of the plane of polarization: $$\phi_{nat}=\alpha l, \phi_{magn}=VlH,$$ where $\alpha$ is the rotation constant, $V$ is Verdet's constant.

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