#### Fundamentals

Having discussed some factors that contribute to a practical upper limit of magnification, let us now consider a low power limit. Suppose we had an eyepiece with 70mm focal length. If we were able to use this with the 150mm f/8 telescope discussed above, it would provide us with only 12X of magnification. This is a very low power for a telescope, similar to many handheld binoculars. With an aperture of 150mm (6 inches), you might expect the view to be much nicer than a pair of binoculars but you would discover something unexpected.

A focused image does not occupy a single point but is really represented by a small disc just above the eyepiece. To see it, you have to move your eye into position so that the disc of light falls upon your eye lens. The size of the disc is called exit pupil and it changes depending on the telescope-eyepiece combination used. If the focused image is too big to fit inside your dilated pupil some light will be lost. Because we are talking about a focused image, gathering light from all across the objective of the telescope, the restriction imposed by your pupil size is not one of simply “clipping the field of view at the edges”. Instead, it serves to effectively reduce the aperture of your telescope because it robs your eye’s retina of a clear view of the full objective and hence, less light than it would have had if the focused image was smaller. Furthermore, if you are using an obstructed telescope design like a Newtonian or Cassegrain reflector, the shadow of the secondary mirror that normally is invisible in the focused image will become noticeable and distracting. You don’t want this.

To avoid these issues, an observer must ensure the exit pupil does not exceed the size of their fully dilated pupil. For most adults, the pupil will open to a maximum of about 7mm and this upper limit will decrease with age. To calculate exit pupil, use this simple equation:

Exit Pupil = (Eyepiece Focal Length)/(Telescope Focal Ratio)

In our example of a 150mm f/8 telescope using a 70mm eyepiece:

Exit Pupil = 70/8 = 8.75mm

At 8.75mm, this telescope-eyepiece combination yields an exit pupil too big for our eye to see. To limit the exit pupil to 7mm with this telescope, we should not use any eyepiece with a longer focal length than 56mm, which would provide about 21X. This represents a practical lower limit to magnification we should use with this telescope. Suppose we had a long-focus refractor with a focal ratio of f/15. In that case a 70mm eyepiece would work just fine, yielding a 4.7mm exit pupil and still giving room to spare.

Why would you want to use such a low power eyepiece anyway? After all, a telescope is supposed to make distant things look bigger. The reason is that some objects extend over very large areas of the sky and to see them you may need a large field of view. Field of view is determined by the diameter of the opening of the eyepiece which is called the field stop. To get a wider field of view you would need a wider field stop and this is why there are different size diameters of eyepieces.

Most telescope focusers purchased today accept either 1.25 inch or 2 inch eyepieces. If you had two 25mm eyepieces of similar design, one in each size, they would both provide the same magnification but the 2 inch eyepiece would provide a much wider field of view because it will have a wider field stop. There are different eyepiece designs however and it is possible to have a 2 inch eyepiece that provides more power and more field of view than our 1.25” diameter 25mm focal length eyepiece. This brings up another characteristic to keep track of, apparent field of view.

Looking in some eyepieces it might be difficult to see the edge of the field of view, where you see the shadow of the confines of the telescope. In eyepieces with a small apparent field of view, it looks like the image is at the end of a dark tube. Most observers prefer the view that does not feel like looking down at the bottom of a tube however. What they prefer is a larger apparent field of view.

Some modern designs of eyepieces have very large Apparent Fields of View, upwards of 100° or more. These eyepieces tend to be expensive and many are of very high quality. However, Apparent Field of View does not make one eyepiece better than others in anything other than a subjective sense. It is just one characteristic to consider when choosing the best eyepiece to use with a telescope. For some applications, simpler designs with fewer lens elements can yield superior views in terms of sharpness, contrast, and purity of color, although at the expense of apparent field of view.

Many observers actually prefer low power views and there are many showpiece objects that need the corresponding wide field of view to be seen in their entirety.  At low power the large exit pupil admits more light into the eye, giving a brighter overall image. Additionally, long focal length eyepieces have comfortable eye relief, which is simply how far from the glass your eye needs to be to see the entire field of view. Many observers find this characteristic appealing. The term “richfield telescope” specifically refers to a telescope made to provide wide fields of view at low power and they are well suited to observing star clusters and nebulae along the Milky Way from a dark site. However, due to the large exit pupil and correspondingly bright image, observing at low power will make seeing small details difficult or impossible and for reasons we will address next, will actually hinder the ability of an observer to see very faint objects a the threshold of visibility.

Magnification is an important factor in how much can be seen at the eyepiece with any telescope, both in terms of detail on bright objects and the mere detection of very faint ones. Understanding the limits of atmosphere and your instruments optics will help guide you determine how much power to use with your telescope, but it is important to remember that magnification is just one parameter that you can control to get the most out of your observing experience. Use it wisely.

## The Mud on Magnification

#### Magnification in Astrophotos

Moving out from the Fovea, rods become the most numerous light detectors. Rods are very sensitive but they do not distinguish color. Rod density is greatest partway to the edge of the retina and because of their sensitivity a common technique used by experienced observers is to intentionally position the light of a faint object on the rods. This technique, called averted vision, allows observers to see fainter objects that might otherwise escape notice. To maximize the effect, the faint objects is viewed 8°-16° toward the nose ensuring the light falls outside of center of the Fovea centralis and away from the blind spot created by the optic nerve. Many rods may be connected to one ganglion cell. This contributes to the overall sensitivity but not to acuity and this is a very important point.

Since our eyes have high acuity with objects bright enough to be detected by cones, poor atmospheric seeing will noticeably degrade an image at medium or high power. Simply put, we can see how bad it is. When we are looking to detect a faint object, we don’t have the acuity to realize how bad the image looks. It’s all about detection.

#### Conclusion

Does magnification affect all objects the same way? Actually no, and the reason why depends greatly on our anatomy. The human eye has two kinds of light receptors, cones and rods. Cones are sensitive to color light and are concentrated in the Fovea centralis, which is the center part of the back of the eye where our eyes acuity is greatest. Their density decreases rapidly moving out toward the edge of the retina. Part of the reason why our acuity is so great in the center of the Fovea is that is where the image created by the eye lens is best, but it also has to do with how the cones are connected to the optic nerve. Each cone connects to a single ganglion cell, which transmits the signal that light was detected by the cone. Cones are great for detecting color, but they do not do well in low light conditions.

Earlier, we mentioned that magnifying an image makes it fainter. Won’t making a faint object even fainter make it harder to see? To see what’s happening here, we need to look at how telescopes focus light from both point sources and extended objects and the surprising results will shed light on an important benefit of using high power on faint objects.

Seen from Earth, a star is essentially an ideal point source of light. No realistic level of magnification will reveal the stars disc, although very high magnification will show an Airy disc, which is simply an optical phenomena related diffraction of light within the telescope itself. Ideally, a star’s light is focused from all over the objective to a single point. Magnifying a point source of light doesn’t spread its light out so it maintains its brilliance. In contrast, the background sky gets darker. This background is never really purely black. Due to scattering of light in the air, it has some amount of brightness usually given in the units of magnitudes/arcsec^2. By magnifying the star you also magnify the background and while the star as a point maintains its brightness the background gets darker, with any one square arc second being made bigger to the eye and spreading out its light. By making the background sky darker, fainter background stars become visible rising about the glow of scattered light. With stars, more magnification allows you to see fainter stars, but as with bright objects, poor seeing eventually limits how deep you can go, scattering the trickle of photons beyond detection.

In the case of an extended object like a faint nebula or galaxy, more magnification spreads its light out just as it does the background sky, making it fainter as well. However, making it appear larger with magnification brings it closer to a critical threshold, that where the acuity of the light sensitive rods can detect it and see its shape and details. In low light, the human eye can’t see small things. It has to be big enough to get noticed, bigger than it would have to be in normal light levels. Through the telescope, an observer needs to make the faint object big enough to see it, even if doing so makes it fainter, and that takes magnification.

#### Another Use for Magnification

The basic purpose of a telescope is to make distant objects appear closer and reveal more detail than would otherwise be visible. To do that, the telescope needs to magnify. However, the use of magnification is also a common point of misunderstanding among many observers. Misleading marketing often targets beginners, convincing them to buy inexpensive telescopes that promise high power views. Among experienced observers there is also confusion with some taking the opposite approach and routinely using too little magnification. How much magnification is appropriate for a particular telescope or target? Here we will discuss the practical limits of magnification as used by recreational observers as well as some techniques to apply the appropriate amount and maximize what can be seen at the eyepiece.

When using a telescope focused on a very distant object, focused to infinity as it is called, the magnification refers to the angular size of the object, not its physical size. For example, the Moon is just over 2,100 miles in diameter and from a distance of about 230,000 miles it appears about 0.5° in angular diameter. If we magnified the Moon’s image ten times, it would appear to be 5° in angular diameter when viewed through the telescope. If it were magnified 100 times, it would extend to cover 50°.

For the visual observer, magnification depends on only two quantities. To calculate the magnification provided by a particular telescope and eyepiece, simply divide the focal length of the telescope by the focal length of the eyepiece using the following relationship.

Magnification = (Focal Length of Telescope)/(Focal Length of Eyepiece)

For example, suppose we are using a telescope with a 1200mm focal length and we have a 25mm eyepiece. Substituting in these values into the above equation yields:

Magnification = 1200mm/25mm = 48

We would say this eyepiece provides 48X of magnification (read “48 times” or “48 power”). It is important to note that this eyepiece will provide a different amount of magnification on a different telescope with a different focal length. For this reason, eyepieces are normally marked with their focal length in mm and it is left to the user to calculate the magnification. If a user does not know the focal length of their telescope, they can calculate it as long as they know the objective aperture and the focal ratio.

Focal Length = Aperture*Focal Ratio

For example, if we didn’t know our telescope had a 1200mm focal length but we did know that it had a 150mm objective aperture (6 inches) and a focal ratio of f/8 (read as “F-eight”), substituting these values yields the following:

Focal Length = 150mm*8 = 1200mm

Telescopes purchased by recreational Astronomers are often provided with only one eyepiece, usually giving a low to moderate amount of magnification. In our example resulting in 48X we could see the entire Moon in one view while being magnified enough to see impressive detail including craters and mountains. Planets will still be small at this power but an observer would easily be able to see the rings of Saturn and the four brightest moons of Jupiter. While 48X is considered low power, it is still more than Galileo Galilei used to discover all these features back in the early 17th Century.

#### High POWER LIMIT

Magnification is an important concept to understand in visual astronomy, but what about those photographs of distant galaxies, nebulae, or the Moon and planets? How much are those magnified? The answer to this question begins to illustrate the differences in approach between visual Astronomy and imaging.

When imaging, the telescope provides an image to a digital sensor with an array of light sensitive pixels. Displayed on screen, the image can be made larger but that really isn’t increasing the magnification. No more detail is revealed by making the pixels of the image larger.

In imaging, magnification isn’t really as useful of a concept as it was in visual Astronomy. Image scale and pixel resolution are the analogous quantities. Image scale tells you how much sky is covered by the sensor in degrees, minutes, or seconds of arc. Pixel resolution, that is how much of the sky is seen by each pixel, is what determines the smallest details that can be detected by the system. You can increase the telescopes effective focal length and the pixel resolution with additional optical elements but as with magnification there are practical limits. Foremost among these limits are those imposed by the atmosphere, the seeing.

Many imagers use reducers which decrease the image scale by reducing the focal length of the system. It also makes the telescope operate at a lower f-stop (in photography terms) or a lower focal ratio (in telescope terms). Another way of saying it is the system will be “faster”, meaning that it will require less exposure to achieve comparable image brightness than at the native focal length when the system was “slower”. Astrophotography has many differences with visual Astronomy as practiced by recreational observers.

# The Oldest Show on Earth

As an image is magnified, the light is spread out over a larger area making it dimmer. An often cited rule of thumb is that a telescope should not be used with greater than 2x the aperture in mm, or 50X per inch of aperture. In our example of a 150mm aperture telescope (6 inch), that would give us 300X as an upper limit. Practically however, such magnification is rarely usable on a scope of this size and a more reasonable 25X-30X per inch of aperture provides a better upper limit. To go beyond this the optical quality must be superb, the instrument in perfect optical and mechanical alignment, and sufficiently cooled to ambient temperature. Additionally, the atmosphere must be very steady to provide a pleasingly sharp image.

Turbulence in the atmosphere is often the limiting factor, blurring a highly magnified image. The steadiness of the air, called seeing, is so important that it is the primary reason that professional observatories are located on mountaintops where there is simply less air to look through and distort the image. For the amateur, the seeing is rarely good enough to allow magnifications approaching the upper theoretical limit of their telescope. Even on larger instruments, 300X often does not provide more details than 200X simply due to the seeing. The image will be bigger but also softer and less appealing. It is important to remember that this affects all telescopes regardless of size or quality, though larger telescopes tend suffer more noticeably in practice.

Does this mean there are never opportunities that you can use more than 300X? Certainly not. Nights of steady air are rare in most places but the views provided by high power on such nights are memorable and will be cherished for a long time. It would also be misleading to say that very high power is not useful, even on nights of average seeing. The trick is to know what to use it for.

It is also important to realize that on any given night, turbulence in the atmosphere is most noticeable near the horizon. With this in mind, waiting until a particular subject is high in the sky (greater than 45° above the horizon is good, near zenith is best) is an effective way to minimize poor seeing. Solar observers will strive to observe well clear of houses, buildings, or pavement which absorb and readily radiate heat, making the air above them unstable. These effects may also last well into the night and the best seeing may be experienced in the early morning hours, shortly before sunrise.

With a visual magnitude of +7.6 the Helix Nebula is one of the closest and brightest planetary nebulas in our sky. At over 25 arcminutes across it is almost as large in apparent diameter as the Full Moon. However, its large apparent size means it actually has a very low surface brightness and it can be a challenge to see. The first three images above (from the left) simulate the view provided in a small telescope at a reasonably dark site and the affects of increasing the magnification. The image on the far left simulates a low power view with a large exit pupil, making the image relatively bright, to include the background sky. By doubling the magnification, as shown with the left middle image, the nebula and background sky are darkened to 1/4 their previous brightness, but the larger area that the Helix now occupies from the observer's perspective makes it more likely to be noticed. Doubling the magnification again (right middle image) further reduces the brightness of the nebula and the background sky, yet by making the nebula appear larger in angular size it also becomes easier to see details. Note how the stars brightness do not change as they are approximately point sources of light. By darkening the background fainter stars become more visible. For comparison, the image at far right is a fully processed long exposure astro-image, incorporating 3 hrs worth of data collected with a DSLR at 900mm of focal length from a dark site. Beginning observers are sometimes disappointed to learn that faint deep sky objects like the Helix do not appear to our eyes as they do in photographs. Such images are only possible to create with considerable effort and expense.