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antoniya [11.8K]
3 years ago
11

Although we have discussed single-slit diffraction only for a slit, a similar result holds when light bends around a straight, t

hin object, such as a strand of hair. In that case, 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???
a= Mm?
Biology
1 answer:
QveST [7]3 years ago
3 0
<h2>Width of hair is "1.96 10⁻⁵ m"</h2>

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 = 5.06/12
  •      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
  • Hence, "the width of the strand of hair is   1.96 10⁻⁵ m" is correct answer

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