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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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hamzaahmeds

Answer:

d = 1.51 x 10⁻⁵ m = 15.1 μm

Explanation:

We will use young's Double Slit formula here:

[tex]Y = \frac{\lambda L}{d}\\\\d = \frac{\lambda L}{Y}[/tex]

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,

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

d = 1.51 x 10⁻⁵ m = 15.1 μm

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