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.