Both lecture and the textbook cover diffraction from a single slit, where light

Question

Both lecture and the textbook cover diffraction from a single slit, where light is sent through a thin opening. But a similar phenomenon occurs when light bends around a thin object, like a human hair. Here the width of the hair is analogous to the width of the single slit. When a beam of light of wavelength 632.8 nm was shone on a single strand of hair, the first dark fringes on either side of the central bright spot were found to be 5.22 cm apart. If the screen is 1.25 meters away, how thick was this strand of hair?

Explanation / Answer

here,

the wavelength of light = 632.8 nm

wavelength = 632.8 * 10^-9 m

y = 5.22 cm

y = 0.0522 m

the screen distance , D = 1.25 m

let the thickness of hair be d

for the first dark fringe

y = wavelength * D/d

0.0522 = 632.8 * 10^-9*1.25 /d

d = 1.52 * 10^-5 m

the thickness of this strand of hair is 1.52 * 10^-5 m

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