When light moves from a medium of a given refractive index n_{1} into a second medium with refractive index n_{2}, both reflection and refraction of the light may occur.
In the diagram above, an incident light ray PO strikes at point O the interface between two media of refractive indexes n_{1} and n_{2}. Part of the ray is reflected as ray OQ and part refracted as ray OS. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θ_{i}, θ_{r} and θ_{t}, respectively. The relationship between these angles is given by the law of reflection and Snell's law.
The fraction of the incident light that is reflected from the interface is given by the reflection coefficient R, and the fraction refracted by the transmission coefficient T. The Fresnel equations may be used to calculateR and T in a given situation.
The calculations of R and T depend on polarisation of the incident ray. If the light is polarised with the electric field of the light perpendicular to the plane of the diagram above (spolarised), the reflection coefficient is given by:
<math>R_s = \left\{ \frac{\sin (\theta_i  \theta_t)}{\sin (\theta_i + \theta_t)} \right\}^2</math>
where θ_{t} can be derived from θ_{i} by Snell's law.
If the incident light is polarised in the plane of the diagram (ppolarised), the R is given by:
<math>R_p = \left\{ \frac{\tan (\theta_i  \theta_t)}{\tan (\theta_i + \theta_t)} \right\}^2</math>.
The transmission coefficient in each case is given by T_{s} = 1  R_{s} and T_{p} = 1  R_{p}.
If the incident light is unpolarised (containing an equal mix of s and ppolarisations), the reflection coefficient is R = ( R_{s} + R_{p} ) / 2 .
At one particular angle for a given n_{1} and n_{2}, the value of R_{p} goes to zero and an ppolarised incident ray is purely refracted. This is known as Brewster's angle.
When moving from a more dense medium into a less dense one (i.e. n_{1} > n_{2}), above an incidence angle known as the critical angle all light is reflected and R_{s}=R_{p}=1. This phenomenon is known as total internal reflection.
When the light is at nearnormal incidence to the interface(θ_{i} ≈ θ_{t} ≈ 0) , the reflection coefficient is given by:
<math>R = R_s = R_p = \left\{ \frac{n_1  n_2}{n_1 + n_2} \right\}^2</math>.
Note that reflection by a window is from the front side as well as the back side, and that the latter also includes light that goes back and forth a number of times between the two sides. The total is 2R/(1+R).
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