Light of wavelength 520 nm passes through a slit of width 0.220 mm. (a) the width of the central maximum on a screen is 8.30 mm. how far is the screen from the slit?

In the single-slit experiment, the displacement of the minima of the diffraction pattern on the screen is given by
(1)
where
n is the order of the minimum
y is the displacement of the nth-minimum from the center of the diffraction pattern
 is the light's wavelength
D is the distance of the screen from the slit
a is the width of the slit

In our problem,


while the width of the central maximum on the screen corresponds to twice the distance of the first minimum from the center, and it is equal to

Therefore the distance of the first minimum from the center is


If we plug these numbers into eq.(1), we can find D, the distance of the screen from the slit: