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?

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