Amaterial having a refractive index of 1.25 is used to coat a piece of glass ( n=1.55). what should be the minimum thickness of this film to minimize reflection of 550nm light.

The minimum thickness of the film is 1.1×10^-7 m.

Explanation:

let Δx be the thickness of the coating.

let n be the refractive index.

let λ be the wavelength of the light.

then, the relationship between the thickness of the coating and different parts making up the functioning of the film is:

Δd + Ф = [m + 1/2]λfilm

where, λfilm = λ/n

Δd + Ф = [m + 1/2]λ/n

but for the minimum thickness, m = 0,because the rays of the light are reflected from a low index material/ medium to higher index material.medium, Φ = 0 and Δd = 2Δx

that is:

2Δx = [1/2]λ/n

Δx = [1/4]λ/n

     = 1/4×[(550×10^-9)/1.25]

     = 1.1×10^-7 m

Therefore, the minimum thickness of the film is 1.1×10^-7 m.

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