Position of the focal plane of a camera on a photo taken with it

[Wimpels]

Say you take a photo down the road. The closer the pebbles were to you the lower their positions are towards the bottom edge of the photograph. The one still closer to you than the one right on the very edge of the photo is not recorded as it falls below the edge of the image, but one surely would be able to extrapolate for its position in some way.

Question:
If I stuck the photograph on a clean sheet of paper, how would I go about to indicate the position of the focal point of the camera relative to the photograph?  Surely it would be a bit below the photo, but how does one find that spot?

Thanks.
Wim

[KeithB]

I think this depends on the angle the of the focal plane.  If the camera is absolutely vertical the position of the focal plane is in the *center* of the image - if I understand you correctly.  If the camera is tilted up or down, then the position of the camera may be out of the frame.

[Wimpels]

Thanks for your reply, Keith.

I did not state fully what I wanted to ask. What I neglected to say is how would one find the position on the photo (or below it on the paper) of the the spot on the ground that is perpendiculary  below the focal point?

In other words, on level ground and with the optical axis of the lens parallel to the ground surface where on the piece of paper, or photo, would the position be that corresponds to that of a pebble on the ground that lies exactly underneath the focal point of the lens?  It surely would be on a vertical line that bisects the photo from left to right because of symmetry considerations, and be below the edge of the photo, but how far below.

I guess it would involve the ratio of the focal length to the width or height of the photo (negative or CCD) in order to normalise it.

Regards.
Wim

[Bob Atkins]

Without doing the mathamatical analysis, my gut feeling is that it would be off at infinity, i.e. you'd need to put the photo on an infinitly large sheet of paper to plot the poition of the point exactly below the lens.

It's all related to rectilinear imaging (see http://www.bobatkins.com/photography/technical/field_of_view.html)

It's sort of like asking where the point would be if it was imaged with a rectilinear lens with a 180 degree field of view. The answer is again, off at infinity because you can't make a rectilinear lens with a 180 degree field of view. It's impossible. You could analyze the case of a lens that had a 179.9 degree field of view (though you couldn't make one!).

[Wimpels]

    Mmmm

[KeithB]

The image is a cone that extends from the focal plane out to infinity.  Your print is "centered" at the focus point, and extends forward and back of that.  if you print the image full size, the focal plane would be off the paper exactly as far as you were when you took the image.  As the print gets smaller, it gets closer and closer to the print, but never reaches gets to the paper.

To do what you want to do I think you will have to do some "forced perspective" like in the "Lord of the Rings" movie or Disneyland.  Use photoshop to tilt the image and then the point of the cone can be manipulated to be on the paper - kind of the opposite of the "vanishing point" you use when making a perspective drawing.

HTH.