Erik Addison , Dec 23, 1997; 09:35 a.m.
At large apertures, image forming light converges obliquely on the film plane. At small apertures it approximates more closely to parallel rays. If a focussed object moves nearer to or further from the camera, the focus point is displaced from the film plane to a point in front of or behind it. The magnitude of defocusing depends on the breadth of the cone of light projected from the rear element & truncated by the film plane. A broad cone (wide aperture) spreads the image more for a given displacement than a narrow cone.
Small apertures do not make an out of focus image perfectly sharp, only sharper than it would have been at a wider aperture but I believe there is an objective criterion for computing depth of field involving circles of confusion.