Exercise 8.1: Antireflection coating: Theory∗ 6 pointsSpecially designed thin films are often used to reduce or eliminate reflection at the boundary between twomedia of different refractive indexes. Consider a thin film of refractive index n2 and thickness d sandwichedbetween media of refractive indexes n1 and n3. Derive an expression for the B element of the M matrix forthis multilayer medium. The multilayer medium can be described by a single dielectric boundary and a propagation followed by a boundary. Show that light incident from medium 1 has zero reflectance if d = λ/4 andn2 =√n1n3, where λ = λ0/n2.

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