Question

Monochromatic light of 605 nm falls on a single slit, which is located 85 cm from a screen. The first dark band appears at 5.4 mm from the center. How wide is the slit?

Answer 1

This is case of fraunhoffer single slit diffraction.
calculate \[\sin \theta = 5.4/\sqrt{85^{2}+0.54^{2}}\]
\[\beta=\pi*b*\sin \theta/\]
condition for first maxima is
\[\tan \beta=\beta\]
which occurs at \[\beta=1.43*\pi\]