The distance between the first and fifth minima of a single-slit diffraction pattern is 0.500 mm with the screen 37.0 cm away from the slit, when light of wavelength 530 nm is used. find the slit width.

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 distance between the first and the fifth minima is
(2)

If we use the formula to rewrite , eq.(2) becomes

Which we can solve to find a, the width of the slit: