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Thin film optical coating

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Thin film optical coating diagram
The reflection from a single-layer interference filter (or mirror) is calculated by use of Snell's law, the Fresnel equations, and trigonometry to find the difference in path lengths between the interfering waves. The result for each polarization is given as well as an average.
α should be given in the n1 material.
Angle α
Index n1
Index n2
Index n3

Path difference
s-polarized reflectivity
p-polarized reflectivity
Average reflectivity
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Thin film optical coatings are used extensively for anti-reflective and decorative purposes. For high-performance dichroic elements, multilayer structures are required, which can not be calculated here.
The p-polarization lies in the plane of the paper. Remember that refractive index is wavelength-dependent. Increasing the angle results in movement to a lower wavelength because of increased path length in the n1 material.