= Solution
Choose cyclic reciprocal units, so the incident and elastically scattered wavevectors have magnitude $1/\lambda$. Place the <reciprocal lattice> origin $O$ at the end of the incident vector from the sphere centre $C$. A reciprocal vector $\mathbf g$ is excited when its endpoint $G$ lies on the <Ewald sphere>, because
$$
\mathbf k_s=\mathbf k_0+\mathbf g,\qquad |\mathbf k_s|=|\mathbf k_0|=1/\lambda.
$$
A specimen tilt rotates the <reciprocal lattice> relative to this construction. The very short <electron> <de Broglie wavelength> makes the sphere nearly flat across several ordinary reciprocal-lattice spacings. In a thin foil, finite thickness $t$ broadens reciprocal points into <reciprocal lattice rods> approximately along the foil normal, with characteristic longitudinal extent $1/t$. A rod may intersect the sphere even when its ideal point is slightly off it. Consequently several reflections can appear simultaneously near a <zone axis>, and thinning changes the excitation tolerance. A small particle has finite-size broadening in other directions too. This geometrical excitation condition does not guarantee a particular spot intensity: <crystal basis structure factors>, specimen thickness and <dynamical diffraction> still matter.
\Image[/past-exam-of-the-mphil-in-micro-and-nanotechnology-enterprise-course-of-the-university-of-cambridge/2017/paper-1-ewald-and-gold.png]
{title=Local <Ewald sphere> intersections and calculated fcc <gold> reflections}
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