Past exam of the mathematics course of the University of Cambridge / 2019 / iii / Paper 338 / 2 / a / vi / Solution

For a large aperture in the standard turbulence model, astronomical seeing is approximately $s=0.98\lambda /r_0$ radians, with Fried parameter $r_0$. Maintaining comparable correction requires a deformable mirror actuator pitch of order $r_0$, so the number of actuators across a diameter is proportional to $D/r_0$ and the total illuminated actuator count is proportional to $(D/r_0{)}^2$. ThereforeLonger wavelengths require fewer actuators and have slightly smaller uncorrected atmospheric angular blur, even though the telescope's diffraction-limited resolution scale $\lambda /D$ increases with wavelength.