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

[ternahan <ternahan@sonic.net>]

another piece in yesterday's NYTimes about painters and lenses and Hockney.
Apparently Hockney and Weschlar(?) were studying a Carravagio in London when
an elderly French man walked by stating that "painting is no good - too much
like a photograph!"
The man was HCB!

> From: Jim Hemenway <jim@hemenway.com>
> Reply-To: leica-users@mejac.palo-alto.ca.us
> Date: Wed, 05 Dec 2001 13:15:16 -0500
> To: rollei@mejac.palo-alto.ca.us, leica-users@mejac.palo-alto.ca.us
> Subject: [Leica] Are there objects points beyond infinity? To infinity and
> beyond!
> 
> 
> 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
> 

- --
To unsubscribe, see http://mejac.palo-alto.ca.us/leica-users/unsub.html