Answer:
The the angle associated with the second dark fringe is 39.9°
Option (a) is correct.
Explanation:
Given:
Wavelength of light [tex]\lambda = 610 \times 10^{-9}[/tex] m
Width of the slit [tex]a = 1.90 \times 10^{-6}[/tex] m
Order of diffraction [tex]m = 2[/tex]
From the formula of single slit diffraction,
[tex]a\sin \theta = m \lambda[/tex]
Where [tex]m =[/tex] order of diffraction, [tex]\theta =[/tex] angle associated with second dark fringe.
[tex]\sin \theta = \frac{\lambda }{a}[/tex]
[tex]\sin \theta = \frac{2 \times 610 \times 10^{-9} }{1.90 \times 10^{-6} }[/tex]
[tex]\sin \theta = 0.6421[/tex]
[tex]\theta = \sin ^{-1} (0.6421)[/tex]
[tex]\theta =[/tex] 39.9°
Therefore, the the angle associated with the second dark fringe is 39.9°
