[Leica] Are there objects points beyond infinity? To infinity and beyond!

[Jim Hemenway <jim@hemenway.com>]

So, was Buzz Lightyear right after all?

> From: "Leonard Evens" <len@math.northwestern.edu>
> Organization: Math Dept, Northwestern University
> Newsgroups: rec.photo.equipment.medium-format
> Date: Tue, 04 Dec 2001 20:13:40 -0600
> Subject: Are there objects points beyond infinity?
> 
> In a discussion of depth of field issues, Eric Boxall, asked me to
> explain how there can be points "beyond infinity".   (Unfortunately I
> accidentally deleted his posting, so I can't respond to it directly.)
> This raises an interesting mathematical point, which of course is
> entirely irrelevant for photography, but since I was asked, let me try to
> respond.
> 
> In the space of our intutition, there are no points at infinity.
> Perhaps the best way to understand this is to concentrate on image points
> instead of object points.   No object in space produces an image point
> closer to the lens than the focal plane.   Indeed, in principle, no image
> point can actually be in the focal plane, but if the object point is
> sufficiently distant, we may consider the image point for all practical
> purposes to be in the focal plane.   That is the meaning in photographic
> optics of saying the object point is at infinity.
> 
> Consider now points in the camera which are between the focal plane and
> the lens.   Are these points the images of any objects points?   Of
> course, the answer is no, but there is a way we can identify points which
> might be considered virtual object points.   For simplicity, think of
> such a point on the lens axis. and consider two rays from that ray to the
> lens.   If the point were the focal point, after refraction, these rays
> would emerge from the lens as parallel rays, which can be thought of as
> intersecting at infinity.  If the point is moved inward towards the lens,
> the rays emerging on the other side of the lens will diverge instead of
> converging.   So there intersection will be somewhere behind the focal
> point.   If the point is close enough to the focal point, that
> intersection will be in back of the camera and indeed quite far away.
> Thus you see that "image points" between the focal plane and the lens can
> be thought of as coming from virtual points in back of the camera.  If
> one were interested in such virtual photography, one could also try to
> analyze the discs in the film plane from such virtual object points and
> decide if they were sufficiently in focus.
- --
To unsubscribe, see http://mejac.palo-alto.ca.us/leica-users/unsub.html