Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, thin object,

Question

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 631.8 nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.20 m away, the first dark fringes on either side of the central bright spot were 5.02 cm apart.

Required:
How thick was this strand of hair?

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Diễm Kiều 5 years 2021-08-02T06:52:22+00:00 1 Answers 55 views 1

Answers ( )

  1. Neala
    0
    2021-08-02T06:53:39+00:00
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    Answer:

    d = 1.51 x 10⁻⁵ m = 15.1 μm

    Explanation:

    We will use young’s Double Slit formula here:

    Y = \frac{\lambda L}{d}\\\\d = \frac{\lambda L}{Y}

    where,

    d = width of strand = ?

    λ = wavelength = 631.8 nm = 6.318 x 10⁻⁷ m

    L = Screen to hair distance = 1.2 m

    Y = fringe spacing = 5.02 cm = 0.0502 m

    Therefore,

    d = \frac{(6.318\ x\ 10^{-7}\ m)(1.2\ m)}{0.0502\ m}

    d = 1.51 x 10⁻⁵ m = 15.1 μm

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