Please agree with me that the size of what you’re looking at is not what matters–it’s the distance. My presbyopia will not allow me to see a penny clearly close up, but that is not a predictor of how well I can see a basketball across the room, which is pretty well. A near-sighted person could be in the opposite situation.
I would guess that those vision testing boxes at DMV have a system of lenses that simulates distance by creating a virtual image that is distant.
I think Squink’s got it right, and your instincts are right. Size alone isn’t a factor in determining ability to see distant objects. If it were, I could put an object right up against my eye and try to see it – but nobody can do that. The boxes I’ve used at the license office clearly have lenses in them. It’s easy to imitate an infinitely distant object – you place the item you want to see at the focal point of the lens in the box. You can also duiplicate an bject at a great but finite distance by adjusting its position a little away from that focal point (although you won’t have to move it far). I have no idea why Marilyn wrote what she did.
Here’s one of the testers they use – Optec 5000 :
In that answer, Marilyn® shows a either lack of knowledge of fundamental optics or an overly-simplistic view of how the eye works.
Her answer only works if the eye worked as a single point with rays emanating out to detect various objects. Similar to how many camera models function in ray-tracing programs. The real world does not work this way.
Instead, each point in a scene is a source of light (usually via reflection). To see what’s at that point, the eye (or any camera) must focus (usually via refraction) that light onto a single point on the retina. Doing this for many points at the same time results in the image you see.
Just thought of another reason she may have answered that way: she’s thinking that the exam is testing angular resolution rather than focusing limits. In that case, foreshortening can work to some extent.
Can’t wrap my head around “infinitely distant” (well, I mean I can parse the words, but …). I’ve got glasses on … is this something I can see for myself if I take them off and hold them at arm’s length or something?
Wouldn’t you imitate it by just having nothing there? An infinitely distant object would be invisible. For a close approximation, you could try reading some of the lettering on the objects left on the Moon: that lettering would appear much larger than the lettering on an infinitely distant licence plate.
Cal means an object at optical infinity, not an object infinitely far away. Optical infinity occurs when the light rays entering the optical system from the object are nearly parallel and the focal distance is equal to the lens system’s focal length.
Yes, I knew that (especially since I myself am shortsighted). Though strictly speaking “nearly parallel” isn’t at infinity, and light from the furthest known galaxies doesn’t come in parallel rays – though of course the angle is not measurable.
Now. now Giles – an infinitely distant object that’s infinitely huge will still subtend a finite angle. More properly, a really big object a really long distance away can still be of finite angular extent. In the limit as it gets further and further away, if it gets bigger at the same rate, it still will be visible. That’s the sense in whiler optical folk use the term, and it has real clounterparts – the Andromeda galaxy is 2.5 million light years away, but it still subtends a visible arc in the sky, because it’s so damned big. For most purposes, the sun is infinitely distant, yet it isn’t invisibly small. Yet Eratosthenes’ method of measuring the earth effectively assumes all rays from the sun are parallel.
Heck, for practical purposes, you can assume objects on the horizon – which are less than 20 miles away in most cases , are infinite if you’re measuring distances. The errors are negligible.
If you place an object at the focal point of a lens and look at it through the lens, it’s as if you’re looking at such an infinitely large infinitely distant object. And not one shrunk to a point.
He she never retracted her book that “proved” that Wiles proof of FLT had to incorrect. She’s put in an addenda, but she never disavowed the book.
If she doesn’t acknowledge an completely erroneous book, correcting all the errors that pop up in her column isn’t going to happen.
Note that in order to fake an infinite-distance sign, you need 3 things: a shrunken image of the sign (which is all she mentioned), change in focal length that more or less works for all people regardless of their eyesight issues (not as easy at it seems) and altering the convergence. The latter is done with prisms in some cases but I’m not sure about DMV boxes.
The rays are not parallel for two reasons: the galaxies have a finite width, and the lens viewing them has a finite width. The first width might be of the order of hundreds of thousands of light years; the second width is of the order of centimeters or meters. But in terms of focussing the image, it’s the second width that counts. So, even if you get more than a point image of the galaxy, and so the apparent angular size of the remote galaxy is measurable, the second angle is about 10^-18 of the size of the first, and hence unmeasurable.
(If you could measure it, you could deduce from it the approximate distance of the galaxy – but we have to deduce that indirectly from other data).
I’m sorry, I must be misunderstanding you. If we get an image of the distant galaxy (so that it’s distinguishable from a point light source), then we are measuring the small angle between the almost-parallel light rays.
No, we’re not. We’re not measuring anything. We’re taking advantage of the fact that objects more than a few tens to several tens of feet away are at “infinity” as far as the optical system is concerned.
Yes, but the lack of parallelism that is relevant to focussing (on the retina, on photographic film, or something similar) is that caused by the width of the lens, not the width of the object being observed. So, if you were photographing that galaxy with an optical telescope theoretically focussed at infinity (and not at the distance of the galaxy), there would be a circle of confusion on your film. However, the circle of confusion is of the order of 10^-18 of the size of the image, i.e., unmeasurable, because other effects (like distortions caused by an inevitably imperfect lens, and distortions caused by the gravitational fields of nearer galaxies and stars) would overwhelm it.
(especially since I myself am shortsighted). Though strictly speaking “nearly parallel” isn’t at infinity, and light from the furthest known galaxies doesn’t come in parallel rays – though of course the angle is not measurable.