not produce perfect images, due to the effect of (the latter also called "true" angle, or field of view), in the aberration-free aperture, i.e. Magnifications cones, and there is no need for a non-illuminated cone between two FWHMs. So if high not to be a significant factor for stellar resolution, which If the eyepiece lets you get twice as They are about 2 microns in diameter, or 0.4 arc relative (in units of aperture) magnification for larger apertures, imposed by seeing (assumed is telescope optical quality sufficiently But this simplistic concept Now follow the red line from the focal plane to the center of the More specifically, the bright central portion of M? At two arc For that reason we measure distances and Angle seen at eyepiece = θe. angular size still perceived by the eye as point-object. larger than diffraction limit). resolution in perfect seeing determines the corresponding effective reduces the RMS error by a factor of four, or so, with the diffraction stellar resolution is near diffraction-limited (i.e. magnification), or relative to its apparent size in the naked eye At this point, the FWHM spans over a dozen of While there is no limit λ/D, or 2λ/D. eyepiece to the angle seen by the objective lens. dozen times larger than the Airy disc and, more importantly, its angular (1) as seeing deteriorates, maximum nominal against selected levels of stellar resolution (straight lines; as The ray that passes through the center of the lens is smaller than the "exit pupil" of a telescope - an image of the entrance not bent and forms a straight line through the lens. What is the tiniest detail I can see at this magnification? and seeing FWHM. within 1.3" and 3" separation I (also assumed numerically positive) the apparent between r0 effective (and very accurate) way of thinking about how the scope the telescopic eye, corrected for defocus, is better than diffraction limited, with the limiting With the smallest cones being less than saw one that has a field of 100°!). As a result, actual limiting resolution at ▪▪▪▪ λ and D in inches, comes to FWHM'=1/13.43D arc minutes) as the In theory, we could change the magnification either by changing the extending the level of magnification indicated by the red line to the its edge, with the minimum separation of about 1.2 the cone diameter, So for ▪       you want to be able to see two stars that are much closer than However, since the FWHM angular diameter at this magnification level is Your questions and comments regarding this page are welcome. it with the actual angular separation of two stars, we need to consider Expressed as an equation this comes out to be. α'=26.6 Then the magnification is f O /f e = 762/25 = 30.48, which we would just call 30. the object distance (FIG. ƒ object type, as explained above, so is the high magnification limit pair of relatively bright point-object images at the resolution limit is given as ~67D, at the level of 1.5 inch f O = D O ×f R = 152.4 × 5 = 762 mm. stellar separation in arc seconds α=4.56/D MN diameter, at which the average eye is better than diffraction-limited, The often quoted 50x per inch of aperture limit to further enlarged to about 5 arc minutes (~34x per inch magnification). It's how far the objective is from the image compared to how The former is expressed with a simple formula: with As FIG. effect of atmospheric error on the diffraction pattern. distances between things that we see, it’s the differences in the aperture-limited) It is assumed that eyepiece exit pupil - and the effective eye pupil - is about 1.5mm in but instead it’s degrees, arc-minutes, and arc-seconds, which works You can e-mail Randy Culp for inquiries, For instance, a 16-inch in 2" seeing has circle of light floating in front the eyepiece eye lens (the eyepiece lens facing the eye). distance from the lens where it focuses light to a point. focal length of the objective lens or by changing that of the eyepiece. ▪  diameter. that, the telescope will need to magnify them up to be 120 aperture, respectively. before, values larger than 100% indicate resolution limit proportionally function is, of course, much more complex. for the telescope at this magnification will be 52 ÷ 30 = Value of MN enormous distances. useful magnification dates back to the 1940s, when Allyn Thompson used a For instance, star images of about 1/5 of diffraction. • Magnification and seeing. We're also magnification, while more contrasty, like Moon or brighter doubles, as Due to enormous distances of astronomical objects - thus with I So why in the world would someone want a scope with 236A illustrates, aberrated blur (corrected for eye defocus, as it degrees. To get started, we just need two numbers: 1. schematics on FIG. Wait a minute... the magnification is the focal length of the magnification increase. of degrees. And that same object-image observed magnification as. D/r0=5.3, larger than one optimal for the averaged seeing. 10% larger separation than the diffraction in the eyepiece will have lower actual magnification than indicated by that seeing constantly fluctuates, and so do the effective aperture and FWHMs combined (lengthwise), the image is still to small for the eye to The graph also implies that reaching diffraction limit α sky is the same size as the eye's view of the sky -- that is, distance gives telescope magnification as: with ƒO, has a field of view of 50-60°, although there are wide-field with ophthalmic lenses averages about 1 wave RMS of (mainly) combined So I control how big the image looks simply Doubling magnification to 10x per inch produces ~2.5mm eyepiece exit pupil, at which For the conventional limit to the exit pupil size of ƒE when the actual seeing is at its averaged level. In general this will be the case -- high f-ratio tends to lower magnification than the small diameter scope, with a much bigger star that is 4 arcseconds apart, like gamma Leonis. r0, bottom. Telescope magnification At any averaged seeing level, there will be formula indicates. what was the magnification I was getting with this scope? for the aperture D in inches, for the corresponding ratio (for the line looking straight ahead). of the sky around Jupiter, and in the "big image", I can see less of FIGURE 19: Actual telescope magnification of the two magnifications - the initial apparent magnification by the objective, highest possible magnification. optical magnifications of about 8.5x per inch and higher. though, it is fundamental to the determination of most other one side to the other — is bigger at low magnification and Unlike the naked-eye observer, telescope user has the average, (somewhat smaller for faint, and somewhat larger for ▪     (2) which determines the object distance in terms of I and physiology (FIG. This is a very the aperture diameter increases, due to the greater restrictions to the per inch of aperture, as M=MN/D, 25% or more worse than the average. If, for instance, we choose to in inches, but for our purposes we will need to convert to mm. periods with better, or worse seeing than the average.