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 633.0nm was shone on a single strand of hair, and the diffracted light was viewed on a screen 1.40m away, the first dark fringes on either side of the central bright spot were 5.34cm apart. How thick was this strand of hair?

Answer 1

a = 16.5 x 10⁻⁶ m = 16.5 μm

Step-by-step explanation:

Here we will use the diffraction equation:

y = mλL/a

where,

y = distance between two consecutive dark fringes = 5.34 cm = 0.0534 m

m = order of diffraction = 1

λ = wavelength of light = 633 nm = 6.33 x 10⁻⁷ m

L = Distance between hair and screen = 1.4 m

a = thickness of hair = ?

0.0534 m = (1)(6.33 x 10⁻⁷ m)(1.4 m)/(a)

a = (6.33 x 10⁻⁷ m)(1.4 m)/(0.0534 m)

a = 16.5 x 10⁻⁶ m = 16.5 μm