22: Problem 22.18

INTRO:
Light of 630nm wavelength illuminates a single slit. The intensity pattern shown in the figure is seen on a screen 2.2m behind the slits.

Part A:
What is the width (in mm) of the slit?
Express your answer to two significant figures and include the appropriate units.

SOLUTION:
givens: 
λ = 630 nm
L = 2.2 m

looking at the Intensity pattern, its clear that the y₁ dark fringes occur at x=1cm and x=2cm so the width of the maxima, is 1 cm
w = 1 cm

Now by rearranging the formula w=2λL⋅1/a, an equation can be formed to solve for the slit width a
a = 2λL⋅1/w = 2⋅630 nm⋅2.2 m⋅1 / 1 cm = 0.28 mm