ChrisR wrote:Huh?
Lenses have interesting behavior, don't they?
An excellent way of thinking about them is the "thick lens model".
Thick lenses act like thin lenses, except that you have to measure the lens-to-object and lens-to-image distances from two
different places called the "principal planes".
What's happening with this lens is that the principal planes are "crossed", meaning that the one used for lens-to-object distances is actually closer to the image than the one used for lens-to-image distances. See discussion
HERE.
Now that we know the FL, it's easy to locate the principal planes by measuring from the object and the image.
Suppose the lens is 40 mm FL and gives 4X when placed on a 150 mm tube. The combination of these facts means that the distance from image to "rear" principal plane is 40*(4+1) = 200 mm, while the distance from object to "front" principal plane is 40*(1/4+1) = 50 mm.
Because the lens is parfocal at 45 mm in front of the lens flange on a 160 mm tube (150 mm from eyepiece focal plane to lens flange), we then have that the "front" principal plane is 5 mm behind the flange and the "rear" principal plane is 50 mm in front of the flange (5 mm behind the object at 4X!).
Locations of the principal planes are determined only by the refracting surfaces, and they stay in fixed positions with respect to the lens as you change the lens-to-object and lens-to-image distances to get various magnifications. So if you're a connoisseur of calculation, you can use the FL and the positions of the principal planes to determine without further experiment where things would have to be in order to get any specific magnification.
Parfocality of the lens at 45 mm is certainly not a coincidence. That was a design requirement for the lens, and the lens designer met it by cleverly figuring out combinations of refracting surfaces that would combine to give the required FL and principal plane placements.
As for positions of the entrance and exit pupils, well, that topic is even murkier. Suffice to say that knowing where the principal planes are tells you essentially nothing about where the pupils are. There are lots of writeups from respected sources that say the pupils are located at the principal planes. Those writeups are misleading at best and completely wrong at worst. For some purposes, you can
pretend that the pupils are located at the principal planes and get the right result. For other purposes, taking that approach gives completely the wrong result , by which I mean that the result predicted by calculation disagrees wildly with the result observed by experiment.
The entrance pupil is simply wherever the aperture appears to be, looking through whatever lens elements are between it and the subject.
Depending on placement of the physical aperture within or even outside the lens, the entrance pupil can be moved from infinity behind the camera, to within the lens, to in front of the lens, to even behind the subject. The latter situation gives inverted perspective -- things closer to the lens look smaller!
ChrisR wrote:Does it matter?
Not really, I'm just curious.
Me too. Curious is good. Every once in a while you find out where Mom keeps the cookies hidden.
--Rik