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15 August, 13:43

A material 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.

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  1. 15 August, 13:49
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    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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