Past exam of the physics 2 paper of the University of Oxford / 2017 / 10 / d / Solution

A feature of transverse size $s=0.03\mathrm{m}$ at height $H=2.0\times 10^5\mathrm{m}$ subtendsChoose a representative visible wavelength $\lambda =550\mathrm{nm}$. For an unobstructed circular mirror, the first Airy disk minimum gives $\Delta {\theta }_R=1.22\lambda /D$, soUsing the single-slit scaling alone would give $D\sim \lambda H/s=3.67\mathrm{m}$; it gives the same metre-scale estimate but omits the circular-aperture factor. Choosing visible wavelengths between $400$ and $700\mathrm{nm}$ changes the circular-aperture estimate to roughly $3.3$–$5.7\mathrm{m}$. These are diffraction-only estimates, not a claim that resolving one stroke guarantees reading arbitrary text with limited contrast or noise.