Remote objects are viewed through a converging lens with a focal length F=9 placed at a distance a=36 in front of the eye. Assume that the radius r of the pupil is approximately 1.5 mm. Choose the correct options.

Let us first neglect the size of pupil, assuming that it is point-like. Obviously, only those of the beams passing through the lens will get into the eye which have passed through point B before they fall on the lens (figure). This point is conjugate to the point at which the pupil is located.

$\frac{1}{\mathrm{F}}=\frac{1}{\mathrm{a}}+\frac{1}{\mathrm{b}},\mathrm{b}=\frac{\mathrm{aF}}{\mathrm{a}-\mathrm{F}}=12\mathrm{cm}$

$\mathrm{R}=\frac{\mathrm{b}}{\mathrm{a}}r\simeq 0.5\mathrm{mm}$,  and the screen must be placed in the plane S with its centre at point B.