Answer
$$s=0.53m$$
Work Step by Step
This is a single slit system, where the slit has a width $a=5.10 \mu m$ and has a screen from the slit at a distance of $d=3.20m$. The incident light has a wavelength of $\lambda=420nm$.
What we need to find is the distance from the central maxima to the second order minima on the screen. We shall denote this as $s$.
The angular position of the minima of the screen in a single slit system is given by
$$asin\theta=m\lambda$$ where $m=2$ for the second order minima.
Hence the angular position is calculated to be
$$5.10*10^{-6}*sin\theta=2*420*10^{-9}$$
$$=> \theta=9.48^{\circ}$$
This can now be used to calculate the distance between the central maxima and the second order minima.
$$tan\theta=\frac{s}{d}$$
Hence $$s=3.20*tan(9.48)=0.53m$$
