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6 May, 12:42

Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, thin object, such as a strand of hair. In that case, a is the width of the strand. From actual laboratory measurements on a human hair, it was found that when a beam of light of wavelength 633.0 nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.25 m away, the first dark fringes on either side of the central bright spot were 5.06 cm apart. How thick was this strand of hair?

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  1. 6 May, 13:39
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    The width of the strand of hair is 1.96 10⁻⁵ m

    Explanation:

    For this diffraction problem they tell us that it is equivalent to the diffraction of a single slit, which is explained by the equation

    a sin θ = ± m λ

    Where the different temrs are: "a" the width of the hair, λ the wavelength, θ the angle from the center, m the order of diffraction, which is the number of bright rings (constructive diffraction)

    We can see that the diffraction angle is missing, but we can find it by trigonometry, where L is the distance of the strand of hair to the observation screen and "y" is the perpendicular distance to the first minimum of intensity

    L = 1.25 m 100 cm/1m = 125 cm

    y = 5.06 cm

    Tan θ = y/L

    Tan θ = 5.06/125

    θ = tan⁻¹ (0.0405)

    θ = 2.32º

    With this data we can continue analyzing the problem, they indicate that they measure the distance to the first dark strip, thus m = 1

    a = m λ / sin θ

    a = 1 633 10⁻⁹ 1.25/sin 2.3

    a = 1.96 10⁻⁵ m

    a = 0.0196 mm

    The width of the strand of hair is 1.96 10⁻⁵ m
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