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At screen coordinate $X$, the propagation length from aperture coordinate $x$ is $[D^2+(X-x{)}^2{]}^{1/2}$. Its expansion has a constant term, a term linear in $x$ giving the observation angle, and a quadratic term of order $x^2/(2D)$. For $|x|\le d/2$, the quadratic wave phase is at most of order $\pi d^2/(4\lambda D)$. Requiring it to be much smaller than one gives the sufficient condition $D\gg d^2/\lambda$; higher terms are then smaller in the paraxial geometry. In the lens arrangement, put the source at the first lens's front focus, illuminate the grating with its collimated output, and put the screen at the second lens's back focal plane. This obtains the angular Fraunhofer diffraction pattern without a physically very distant screen.

The slit pitch is $p=1/(200\mathrm{m}{\mathrm{m}}^{-1})=5.00\mu \mathrm{m}$. Normal-incidence maxima satisfy $p\sin \theta =m\lambda$. Thus $\sin {\theta }_3=0.276$ and, using rectilinear focal-plane geometry,The paraxial result $x_3\simeq fm\lambda /p=\pm 82.8\mathrm{mm}$ is a roughly 4% lower approximation; an actual wide-angle lens's mapping depends on its design. The angular result does not depend on that convention.

For $N$ uniformly illuminated equal slits of width $w$, the diffraction intensity has the formHere $C$ is unchanged when the incoming intensity is fixed. The broad single-slit diffraction envelope multiplies the narrow grating orders. At a principal maximum,The fixed-illumination grating peak change with slit width gives the changes from $w=1.0$ to $1.5\mu \mathrm{m}$ areThe central peak increases by 125%, while the third-order peak decreases by about 89.4%. Separate normalizations to each central peak would hide this effect. The following width-specific solutions and profiles use a common incoming normalization.