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
It is likely that the researchers are studying the function of this gene that encodes for a lipase enzyme. In molecular biology, it is common to use cell lines which are transfected with constructs that contain genes or gene regions in order to study the function of these genes (or genetic elements
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