Diffraction angle goes as wavelength over aperture, so halving the opening doubles the spread — squeezing a beam tighter makes it fan out wider, not narrower.
It sets a hard floor on how sharp any optical instrument can be. A pinhole camera cannot be improved indefinitely by shrinking the pinhole, and a telescope resolves finer detail only by getting physically bigger — no amount of magnification substitutes for aperture.
The relationship is for the far field, where the screen is many aperture-widths away; close to the opening the near-field pattern looks quite different. It also assumes the aperture is much larger than the wavelength — comparable sizes need a full electromagnetic treatment, not this approximation.
At 5 ×λ the rule says 0.2 rad and the exact answer is 0.2014 rad — 0.67% low. It holds to within 5% above 1.9 ×λ, and drifts below it.
θ = λ/a is the small-angle form of sinθ = λ/a, and it holds while the slit is many wavelengths wide. Squeeze it to a couple and the approximation understates the spread badly; at one wavelength the true answer is a full 90° and the rule says 57°.
The rule against the exact answer, computed across the range. Inside the shaded band the shortcut is close enough to use; outside it, reach for the calculator.
Estimate with the rule, then check it against the calculator that models it properly.
Open Refraction & Diffraction Calculator →Diffraction angle goes as wavelength over aperture, so halving the opening doubles the spread — squeezing a beam tighter makes it fan out wider, not narrower. It sets a hard floor on how sharp any optical instrument can be.