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
