If you were to double the width of a single slit, by how much would you change the width of the central maxima?

Answer: the width of central maxima decrease a factor 0.5

Explanation: To explain this results we have to consider the relationship given for the locations of the first dark fringes asides to central maximum ofone lit difraction as:

sin θmin = + / - λ/a where a is the slit width so the width on the screen is approximately given by:

y1 = Lsin θmin where L is the distance to the screen

Finally we have the full width on the screen is: 2y1 = Lλ/a

if we double the width, we have 0.5 of the full width of the central maximun given by the initial slit