= Solution
An ordinary passive primary must keep its optical figure while the direction of gravity relative to the mirror changes as the telescope tracks. A thin unsupported disk bends enough to introduce <wavefront errors>, degrading the <point spread function>. Increasing thickness strongly raises its resistance to bending.
For an isotropic <elastic plate> of thickness $t$, <Young's modulus> $E_Y$ and <Poisson's ratio> $\nu$, the flexural rigidity is $\mathcal B=E_Yt^3/[12(1-\nu^2)]$. Under its own weight the load per area scales as $\rho g_0t$. With support spans of order the diameter $D$, plate bending therefore gives
$$
\boxed{h\sim\frac{\rho g_0D^4}{E_Yt^2}.}
$$
Numerical coefficients depend on the support and boundary conditions. A larger $t$ greatly reduces gravitational sag, even though it adds weight. Near normal incidence a mirror displacement $h$ changes <optical path length> by approximately $2h$, so surface errors must be much smaller than the observing <wavelength>. \b[Thickness provides passive stiffness needed to preserve the mirror figure.]
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