A beam of light of lambda=600nm from a distance source falls on a single slit 1mm wide and the resulting diffraction pattern is observed on a screen 2m away. The distance between first dark fringes on either side of the central bright fringes is:

Wavelength of light, $\lambda = 600 \text{ nm} = 600 \times 10^{-9} \text{ m}$
Slit width, $a = 1 \text{ mm} = 1 \times 10^{-3} \text{ m}$
Distance to the screen, $D = 2 \text{ m}$

The position of the $m$-th dark fringe from the center of the screen is given by:

where $m = \pm 1, \pm 2, \dots$ for dark fringes.

For the first dark fringe above the central maximum, $m=1$:

For the first dark fringe below the central maximum, $m=-1$:

The distance between the first dark fringes on either side of the central bright fringe is $Y = y_1 - y_{-1}$.

Since $1 \text{ m} = 1000 \text{ mm}$:

This matches option (b).

The final answer is $\text{(b) } 2.4 \text{ mm}$