How Does a Narrow Slit Affect Laser Beam Divergence?

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what is the effect of placing a slit of say one tenth of an inch infront of a laser beam (3 inch dia )with a divergence of say one degree upon the divergence of the emanating beam?(slit placed symmetrically along the beam axis) ? would the emanating beam also be of the same divergence ?
 
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The divergence angle would increase somewhat, but not appreciably in this case.

For visible light, a 0.1" slit creates a diffraction angle of approximately (550 nm)/(0.1") = 2 x 10-4 radians or 0.01 degrees (ballpark figure)

Since that's a lot smaller than the initial 1 degree divergence angle, the effect is pretty small for visible wavelengths.