Solution
Given,
Distance between two slits (d) = 0.45 mm = 0.45 x 10^-3 m,
Distance between slits and the screen (D) = 75 cm = 0.75 m,
Wavelength of light (λ) = 500 nm = 500 x 10^-9 m = 5 x 10^-7 m,
Fringe width (β) = ?
Since, in the interference pattern due to the slits, all the fringes are equally spaced, the distance between the second and thrid dark lines is the fringe width which is given by,
\(\beta=\frac{\lambda D}d=\frac{5\times10^{-7}\times0.75}{0.45\times10^{-3}}\)
= 0.833 × 10-3 m
Hence, the distance between the second and the third dark lines of the interference pattern is 0.833 × 10^-3 m.