Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / A4 / Solution

The photon wavelength is $\lambda =hc/E=3.5424\times 10^{-11}\mathrm{m}$. The exact half-period zone radii for incident plane waves are chosen so that the path to the axial focus increases by $\lambda /2$ per zone:Transmit alternate zones and block the others, with $r_0=0$. For $f=1.00\mathrm{cm}$, $r_1=0.5952\mu \mathrm{m}$. The number of zones is a design choice: 100 zones give outer radius $5.952\mu \mathrm{m}$ and outermost width about $29.8\mathrm{nm}$. Adjacent open zones then arrive in phase at the principal focus.

The blocking material must be sufficiently opaque at 35 keV; no attenuation coefficient or fabrication thickness is specified. A binary amplitude plate also has zero-order transmission and other odd-order foci, so an aperture/order stop may be needed. The principal focal length is chromatic, varying as $1/\lambda$ for fixed radii.