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Fresnel Equations

Equations that describe the reflection and transmission of light at an interface between two media, considering both angles and wavelengths. \frac{I_{\theta}}{I_0} = R(\theta) + T(\theta)
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The statement of the theorem

Let Ei,Hi\mathbf{E}_i, \mathbf{H}_i be the incident fields and Er,Hr\mathbf{E}_r, \mathbf{H}_r be the reflected fields in Medium 1, and Et,Ht\mathbf{E}_t, \mathbf{H}_t be the transmitted fields in Medium 2. Assume the interface lies in the xyxy-plane. The boundary conditions require continuity of the tangential components of E\mathbf{E} and H\mathbf{H}. Define the relative parameters ϵr1,μr1\epsilon_{r1}, \mu_{r1} and ϵr2,μr2\epsilon_{r2}, \mu_{r2}. The reflection coefficients rsr_s (s-polarization, perpendicular to the plane of incidence) and rpr_p (p-polarization, parallel to the plane of incidence) are given by:\n\nFor ss-polarization:\nrs=η2cos⁡θi−η1cos⁡θtη2cos⁡θi+η1cos⁡θtr_s = \frac{\eta_2 \cos \theta_i - \eta_1 \cos \theta_t}{\eta_2 \cos \theta_i + \eta_1 \cos \theta_t}\n\nFor pp-polarization:\nrp=η2cos⁡θt−η1cos⁡θiη2cos⁡θt+η1cos⁡θir_p = \frac{\eta_2 \cos \theta_t - \eta_1 \cos \theta_i}{\eta_2 \cos \theta_t + \eta_1 \cos \theta_i}\n\nWhere ηk=μrk/ϵrk\eta_k = \sqrt{\mu_{rk} / \epsilon_{rk}} is the intrinsic impedance of Medium kk, and θi\theta_i and θt\theta_t are the angles of incidence and transmission, respectively, related by Snell's Law: sin⁡θi/sin⁡θt=ϵr2/ϵr1\sin \theta_i / \sin \theta_t = \sqrt{\epsilon_{r2} / \epsilon_{r1}}. The transmission coefficients tst_s and tpt_p are related to the reflection coefficients by tk=1+rkt_k = 1 + r_k (assuming μr1=μr2=1\mu_{r1} = \mu_{r2} = 1).
Source: Wikipedia