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26 January, 06:20

What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 535 nm? The index of refraction of the film is 1.32, and there is air on both sides of the film.

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  1. 26 January, 09:03
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    0.203 micro meter

    Explanation:

    for destructive interference that appearsblack, use the formula

    2 t = m λ / u (where m = 0 1 2 3 ... is order of minima)

    where t = tickness,

    u is the ref index = 1.32

    Wavelenth λ = 535*10^-9 meter

    for t (minimum) m = 1 (as m=0 is ruled out as t>0)

    t = 1 * 535*10^-9/2*1.32

    t (min) = 202.65*10^-9 meter

    OR

    t (min) = 0.203*10^-6 meter = 0.203 micro meter
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