Answer
increasing the amount of slits will result in a decrease of the half-widths
Work Step by Step
This is a diffraction grating, so we can look at equation (36-28) to see how the half-widths, $\Delta \theta_{hw}$, is affected by increasing the amount of slits, N. Therefore;
$$\Delta \theta_{hw}=\frac{\lambda}{Nd\cos \theta} $$
We can see that increasing the amount of slits, N, will result in a decrease of the half-widths, $\Delta \theta_{hw}$.
