Close, but not quite correct:
The front group called the objective group focuses a reversed image in front of the middle lens group often called the erector group. Sometimes this objective group can be moved back and forth like a camera lens to focus the target image at different ranges at precicely the same place in front of the erector lens group behind it.
The erector group focuses the image from the objective group reversed again, or "erected" behind it in front of the rear group called the eyepiece group where the reticule is usually located. The inner tube holding the erector lenses is what's moved by the elevation and windage adjustments.
The eyepiece group focuses on the reticule where the now erect image is and it's adjusted for the shooter's eye's optical characteristics so it and the reticule appears sharp and easy to see.
Variables have two sets of lenses in their erector group. Those two groups move back and forth different amounts changing the image size on the reticule to make it appear closer or further depending on the magnification selected on the zoom ring. As their lens mount mechanics have tolerances, so do their alignment with each other. As both lens groups move back and forth as the scope's power is changed, those two groups will not do so exactly the same. So, the image will move around a bit as the scope power changes. Good variable scopes will have no more than about 1/4 MOA image shift on the reticule in a figure 8 pattern as the power's changed. Others will have as much as 3/4 MOA or more.
For absolute precision, use a fixed power scope. If one must use a variable, then a small amount of slop's going to exist in how the target image is focused on the reticule, so set the scope to maximum power to hold the erector lens groups as solidly as possible when best precision is desired.
A scope's magnification is calculated by dividing the focal length of the combined objective and erector lens groups by the focal length of the eyepiece group. The eyepiece group for all rifle scopes has about a 2 inch focal length which is good for most human eyes. So, a 20X scope's objective-erector lens focal length is 40 inches. But the optical properties of telescopes are such that the physical length of them is shorter than their longest focal length set of combined lens groups. That's how a 20X rifle scope can be only 15 inches long.
A fixed power scope needs at least 3 lens groups. Better quality scopes have at least 2 individual lens elements cemented together in each group.A plain Jane fixed scope only has two lenses-one at each end. A fixed power with AO adds one more. A plain variable has at least three lenses, and the fourth for the AO or paralax ring.
The front group called the objective group focuses a reversed image in front of the middle lens group often called the erector group. Sometimes this objective group can be moved back and forth like a camera lens to focus the target image at different ranges at precicely the same place in front of the erector lens group behind it.
The erector group focuses the image from the objective group reversed again, or "erected" behind it in front of the rear group called the eyepiece group where the reticule is usually located. The inner tube holding the erector lenses is what's moved by the elevation and windage adjustments.
The eyepiece group focuses on the reticule where the now erect image is and it's adjusted for the shooter's eye's optical characteristics so it and the reticule appears sharp and easy to see.
Variables have two sets of lenses in their erector group. Those two groups move back and forth different amounts changing the image size on the reticule to make it appear closer or further depending on the magnification selected on the zoom ring. As their lens mount mechanics have tolerances, so do their alignment with each other. As both lens groups move back and forth as the scope's power is changed, those two groups will not do so exactly the same. So, the image will move around a bit as the scope power changes. Good variable scopes will have no more than about 1/4 MOA image shift on the reticule in a figure 8 pattern as the power's changed. Others will have as much as 3/4 MOA or more.
For absolute precision, use a fixed power scope. If one must use a variable, then a small amount of slop's going to exist in how the target image is focused on the reticule, so set the scope to maximum power to hold the erector lens groups as solidly as possible when best precision is desired.
A scope's magnification is calculated by dividing the focal length of the combined objective and erector lens groups by the focal length of the eyepiece group. The eyepiece group for all rifle scopes has about a 2 inch focal length which is good for most human eyes. So, a 20X scope's objective-erector lens focal length is 40 inches. But the optical properties of telescopes are such that the physical length of them is shorter than their longest focal length set of combined lens groups. That's how a 20X rifle scope can be only 15 inches long.
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