Marc: Thanks for your more detailed explanation (see below my message) of what you intended to say. Sorry to be pernickety, but I still need to clarify one point.
Ref: http://research.opt.indiana.edu/Library/INEye/IndianaEye.html Diagram labelled "General Chromatic Eye" (middle diagram) You wrote: >In order for the image to be inverted, that means that light from the top >of the object (grandma's hair) has to wind up on the bottom of the image, >and light from her shiny shoes on the top of the image; it's also reversed >left to right. But the light falling on cornea is *not* inverted. Thus, it has >to get inverted inside the eye. I take it that when you say the "light" is inverted you mean that in a diagram such at the one in question (in which the only relevant rays for our purposes are the two that go from the top and bottom of the object in a straight line to the corresponding points on the retina), the "top" ray has crossed over the other one and has become the "bottom" ray. But it is important to appreciate that this diagram is not intended to show *how* an image is formed at the retina. The crossover point here is not "where the image is inverted". There is no point where the image is inverted in the human eye lens system. The inversion is produced by the combined effect of a multitude of rays from each single point on the object, the vast majority of which do not pass through N, forming a corresponding point image on the retina, with a multitude of image points being produced (by rays originating from corresponding points down the object) in such a way that the image is inverted. See the very first diagram, then the second diagram in section 4, at http://www.glenbrook.k12.il.us/GBSSCI/PHYS/CLASS/refrn/u14l5da.html and imagine the two combined. What you have described in the above quote, Marc, is how an image is formed in a pinhole camera, where *all* the rays cross at the same point (the pinhole). In such a case one could say that the inversion occurs at the crossover point (because rays that originated at relatively high points on the object are, after the crossover point, then *below* rays that originated at relatively lower points on the object). But this does not represent the process by which an inverted image is formed with the human eye lens system. What I guess you are intending to convey is the simplified lens diagram one uses, e.g., to obtain the formula for the magnification of a convex lens. The only relevant diagram I can find is Fig. 3 at http://www.physicslabs.umb.edu/Physics/sum06/Exp6_182_Sum06.pdf#search=%22lens%20%2B%20%22magnification%20formula%22%22 where the lines PQP' and OQO' correspond to rays from grandma's hair and her shoes in your example above. A diagram showing only these two rays is useful to obtain (using the properties of similar triangles) the formula for magnification, but does not show how an image is actually formed by the lens, or indeed how the inversion is actually produced. For that you need to show multiple rays from a single point on the object passing through a (relatively) wide range of angles at the pupil (and preferably also the same thing from other points on the object, to show how the image points build up). Incidentally, the diagram in question at http://research.opt.indiana.edu/Library/INEye/IndianaEye.html serves to show that, as Marc has said, the size of the pupil is too large for the eye system to function as a pinhole camera. Allen Esterson Former lecturer, Science Department Southwark College, London http://www.esterson.org/ ---------------------------------------------------------- Date: Mon, 9 Oct 2006 06:42:45 -0500 Author: "Marc Carter" <[EMAIL PROTECTED]> Subject: Re: vision Q ---------------------------------------------- >Date: Tue, 10 Oct 2006 13:10:32 -0500 >Author: "Marc Carter" <[EMAIL PROTECTED]> >Subject: RE: [SPAM] - Re: vision Q (pinhole camera issue) > Alan, and all -- > > The problem I think with my explanation is that I'm not being clear when > I talk about a collimated point-light source (the rays are parallel, as > if the object were infinitely far away) versus light incident at cornea > from a spatially-extended object (like a grandmother, standing in front > of her house) that is relatively close, and the idea that the light > "crosses" at all. =20 > > First, my understanding of nodal points: Images of objects on the retina > are inverted. You can look at them and see it. In order for the image > to be inverted, that means that light from the top of the object > (grandma's hair) has to wind up on the bottom of the image, and light > from her shiny shoes on the top of the image; it's also reversed left to > right. But the light falling on cornea is *not* inverted. Thus, it has > to get inverted inside the eye. The "nodal point" is the location at > which the light from, say the top of her head and heading to the lower > part of the image crosses the light heading from her feet to the top of > the image. This point is usually depicted just posterior to the lens, > and where exactly it is will depend on the light incident at retina (how > far away the object is) and the current state of lenticular > accommodation. You can see it here > <http://research.opt.indiana.edu/Library/INEye/IndianaEye.html>. > > Where I am being unclear in this is in suggesting that the light really > crosses -- it doesn't. The nodal point we use in some calculations to > simplify the optics of the eye; its use requires that we treat the light > incident at retina as if it had traveled in a straight line from the > object. Top of object to bottom of retinal image, bottom of object to > top at retina. You can use this for computation of visual angle, things > like that. But it is merely a useful fiction. > > Light from a collimated point source will not converge until it reaches > retina -- if the eye's optics fit it, and assuming that the lens is > accommodated to infinity (completely relaxed). This is what we used to > do with a magnifying glass on a summer day: project a small image of the > sun onto a surface, which would then get pretty darned hot (it > effectively sums the light falling on the area of lens and concentrates > it to a near-point, which gets pretty hot). (This is an interesting > thing, too, about lasers: even though the laser is low-power, your eye > concentrates into a point all the light over the area of the pupil. > Don't look into lasers, especially if your pupils are dilated...) > > The thing is that the nodal point is a "virtual" (bad choice of words) > point because the light really doesn't "cross" in such a simplified > manner. Truly, the image of every point on grandma is imaged on retina > as a point, and thus there is no "crossing" at all -- just like the > light from the collimated source. It *apparently* crosses because the > image is inverted, and the nodal point represents that location where it > would cross if the light were traveling in a straight line -- which, of > course, it is not. > > I'm sorry for being unclear earlier. > > m > > ------- --- To make changes to your subscription go to: http://acsun.frostburg.edu/cgi-bin/lyris.pl?enter=tips&text_mode=0&lang=english
