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Anti-reflection Coating

A linearly polarized plane wave of wavelength lembda, is travelling in air and ia incident normally on a plane sheet of glass. Show that the ratio of the reflected to the incident electric field amplitude is


where n(air) and n(glass) are the refractive indices of air and glass respectively.

The glass sheet is now coated on the incident side with a material with a refractive index n(coat) = squareroot((n(air)*n(glass))) and a thickness d = lembda/4. Prove that there is now, in principle, no reflected power.

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