A single slit of width a is illuminated by a monochromatic light of...

For the first minima

$asin\theta = \lambda$

The given data is

$\theta = 30 ° \lambda = 600nm$

The value of $a$ is

$a = \dfrac{\lambda}{\sin 30 °} = \dfrac{600 \times {10}^{- 9}}{\dfrac{1}{2}} = 1 . 2\mu m$