Question

a single slit is the simplest means to produce an interference pattern from light waves. how does the pattern of light and dark bands change as the slit gets wider?

Answer 1

One must consider the phase difference between each side of the slit:

One can write Δ = W sin θ where Δ is the phase difference between light leaving opposite sides of the slit, W = slit width, and θ is the angle of difraction

As the slit gets wider (W increases) and for a given phase difference the angle of difraction will decrease

The bands on the screen will be closer for a wider slit