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?

Answer 1

d = 1.51 x 10⁻⁵ m = 15.1 μm

Step-by-step explanation:

We will use young's Double Slit formula here:

`Y = (\lambda L)/(d)\\\\d = (\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 = ((6.318\ x\ 10^(-7)\ m)(1.2\ m))/(0.0502\ m)`

d = 1.51 x 10⁻⁵ m = 15.1 μm