Although we have discussed single-slit diffraction only for a slit, a similar re

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 632.8 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 5.22 cm apart. How thick was this strand of hair?

Explanation / Answer

The diffraction pattern for a hair is the same as for a slit of equal width. The separation of the dark fringes is twice the distance from center to either fringe, so

sin(theta) = 2.61 / sqrt(2.61^2 + 125^2) = 0.02087

a*sin(theta) = m

a = m / sin(theta) here m = 1

a = (632.8 x 10^-9 ) / 0.002087

a = 29.88 um

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