A flat screen is located 0.55 m away from a single slit. Light with a wavelength of 544 nm (in vacuum) shines through the slit and produces a diffraction pattern. The width of the central bright fringe on the screen is 0.052 m. What is the width of the slit?

The diffraction pattern is given as

Sinθ = mλ/ω

Where m=1,2,3,4 ...

Now, when m=1

Sinθ = λ/ω

Then,

ω = λ/Sinθ

The width of the central bright fringe is given as

y=2Ltanθ. From trigonometric

Then,

θ=arctan (y/2L)

Given that,

y=0.052m

L=0.55m

θ=arctan (0.052/2*0.55)

θ=arctan (0.0473)

θ=2.71°

Substituting this into

ω = λ/Sinθ

Since λ=544nm=544*10^-9m

Then,

ω = 544*10^-9/Si. 2.71

ω = 1.15*10^-5m.