Answer
$d=11.1 \mu m$
Work Step by Step
Beta is defined as $$\beta=\frac{\pi d}{\lambda}sin \theta$$ Using $sin\theta$ as the x-axis and $\beta$ as the y-axis allows the slope of the regression to be equal to $\frac{\pi d}{\lambda}$. The slope of the line can be found using $$m=\frac{\Delta y}{\Delta x}=\frac{80.0rad}{1}=80.0rad$$ Solving for the slit separation distance yields $$d=\frac{m\lambda}{\pi}$$ Using known values of $m=80.0rad$ (slope) and $\lambda = 435 \times 10^{-9}m$ yields a $d$ value of $$d=\frac{(80.0rad)(435 \times 10^{-9}m)}{\pi}=11.1 \mu m$$
