In a Young’s double slit experiment, two slits are...

The position of first minima is

$y = \dfrac{\lambdaD}{2 \times a}$($y$ is height of the point from the axis passing through the mid-point of ${A}_{1}\text{and}{A}_{2}$)

Since the first minima is in front of the slit as shown in the figure,

$\dfrac{\lambdaD}{2 \times a} = \dfrac{a}{2}$

$⇒ a = \sqrt{\lambdaD} = \sqrt{800 \times {10}^{- 9} \times 5 \times {10}^{- 2}} = 2 \times {10}^{- 4}m = 0 . 2mm$