What width slit will produce a central maximum that is 3.00 cm wide on a screen 1.80 m from the slit?

The central maximum extends to the first minimum on either side.

So the first minimum occurs at 3cm / 2 = 1.5cm = 0.015m to the side from the center of the central maximum. 

Now using the formula,
λ = a(y/L)

Where a is the width of the slit, y = distance of first minimum from center, L = distance of screen from slit, and λ = wavelength of the light that strikes a single slit at normal incidence which is unknown here.

a = L x λ/y 
a = 1.80 m x (λ / 0.015 m) 
a = 120 λ 

Use the value of λ for any light and you get the width of slit.

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c) both a and b.

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