Past exam of the physics 2 paper of the University of Oxford / 2021 resit / 7 / c

Two nearby directions separated by ${\theta }_R$ focus at transverse separation $s\simeq f_m{\theta }_R$. To avoid a receiver covering both geometric image centres at once, its diameter $d$ should not exceed this separation along the orbital direction:This is the usual receiver-size estimate from angular resolution. The Airy disk first-minimum diameter is $2f_m{\theta }_R=53.8\mathrm{mm}$, but that is a spot-size definition, not the same as the receiver's allowed angular acceptance. At the Rayleigh criterion, the images already overlap; integrating over a finite receiver further reduces contrast. Consequently $26.9\mathrm{mm}$ is an order-of-resolution upper scale, not a sharp universal boundary for a specified signal discrimination probability. A detailed limit would require the receiver response and a resolving criterion.