A parallel beam of monochromatic light of wavelength 450 nm passes through a long slit of width 0.2 mm. The angular divergence in which most of the light is diffracted is given by $\mathrm{k} \mathrm{x} {10}^{-3} \mathrm{rad},$then the value of 'k' is

Given, 

    $$\begin{gathered} \lambda = 450 nm \\ b = 0.2 mm \end{gathered}$$

For angular divergence, $\theta = \pm n\frac{\lambda }{b}$

Most of the light is diffracted between the two first order minima, n = 1

Which occurs between $\theta = \pm \frac{\lambda }{b}$

$\Rightarrow \theta = \pm 2.25 \times {10}^{-3} radian$

Hence angular divergence = $2\theta = 4.5 \times {10}^{-3} radian$