Problem 5.38

A thin converging lens with aperture ratio \(D: f=1: 3.5\) ( \(D\) is the lens diameter, \(f\) is its focal length) provides the image of a sufficiently distant object on a photographic plate. The object luminance is \(L=260 \mathrm{~cd} / \mathrm{m}^{2} .\) The losses of light in the lens amount to \(\alpha=0.10 .\) Find the illuminance of the image.