Double Slit Interference Pattern

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I am trying to calculate how wide of a screen you would need in order to observe an interference pattern produced by Young's original real-life double slit experiment. He cut a single narrow slit (width ds) in a window shade, admitting a narrow sliver of sunlight into a dark room. He inserted a colored filter into the sunbeam that transmitted a narrow band [tex]\Delta[/tex][tex]\lambda[/tex] of wavelengths around a center wavelength [tex]\lambda[/tex]0. A distance Ls away, the filtered beam illuminated an opaque screen in which he had cut 2 identical slits, each of width w, seperated by distance d > w. He observed the interference pattern on a screen located distance L beyond the slits.

Ls = 2 m
w = 0.1mm
d = 0.25 mm
[tex]\lambda[/tex]0 = 0.5 microns
L = 4 m
r = radius of pattern (or screen needed)

Here is what I did, and my results seem too small.

[tex]\theta[/tex] = 1.22([tex]\lambda[/tex]/d) = r/L

Solving for r I got:

r = 1.22(L[tex]\lambda[/tex]/d) = 4.88 mm

Like I said, this doesn't seem correct. It seems like the entire pattern will spread out more. How can I determine the width of the pattern?
 

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