How Cameras, Binoculars and Telescopes Work
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— Albert Nagler
CEO, Tele Vue Optics

Let's discuss the meaning of the specifications usually supplied so the easily understood concepts can be applied to telescopes, which often have confusing, if not misleading specs and jargon.

Cameras

Camera lenses have two major specifications, focal length and f/#.

1. Focal Length

The focal length determines the size of the image on the film. If we consider a zoom lens you know that the 35mm setting is "wide angle", 50mm is" normal" and 135mm is "telephoto." Focal length, for a given film size (such as 35mm) determines the "field of view", a specification usually ignored or unstated directly. " Field of view" is of course the angle of view seen in the real world and is inversely proportional to focal length. The 135mm setting has the highest magnification and smallest field, while the 35mm setting has the lowest magnification and the largest field, in fact almost 4 times the field size (135/35) and 16 times the field area!

Many people of course confuse f/# and focal length and think that a change in the f/# setting affects the image size in some magical way. It's only the focal length that affects image size and field size.

2. Focal Ratio, or f/#

Usually written as a ratio, (1:2 for example, on the lens barrel means f/2), this gives the "fatness" of the cone of light that reaches the film. "Fatter" cone, more light, faster exposure. f/# is actually the ratio of the focal length to the effective diameter of the lens. A 50mm f/2 lens has an effective lens diameter of 25 mm. ( Remember that 25.4 mm equals 1 inch - a useful fact when we discuss telescopes, where lens diameter is sometimes given in inches and the focal length in millimeters.)

Most people instinctively appreciate that an f/2 lens is faster than an f/4, but may not know that it's 4 times faster! Also, there's a misconception that the f/2 lens is sharper. (Theoretically possible, but rare in practice.)

While f/# is a critical specification for cameras, where f/#, film speed and subject brightness are exposure variables, we shall see that it has no direct effect on brightness of images viewed through a telescope. A shocking statement to my photographer friends who've recently become "telescope nuts."

A big thank you now to the binocular industry, which has developed meaningful product specifications, never, ever mentioning f/ratios.

Binoculars

Not everyone thinks of binoculars as 2 parallel telescopes, but it sure is handy when explaining how a telescope works. Neglecting the prisms which turn the image right-side up, the binoculars consist of an objective to form an image just like a camera lens, and a magnifier to view the image directly instead of film to capture the image. We call the magnifier an eyepiece, or ocular.

The ratio (there's that word again) of the focal length of the objective to focal length of the eyepiece gives the magnification or power of the binocular or telescope.

Binocular Specs

6 x30, 7 x35, 7 x50, 10 x50 etc. How nice to have meaningful specs without confusing f/#'s. A 7x35 means 7 power having a 35mm objective lens aperture (diameter). Notice that nobody said it's 7 power because the objective has a focal length 7 times that of the eyepiece, or that maybe it came from a 140mm focal length objective used with a 20mm focal length eyepiece. Or, that the 140mm objective with a 35mm diameter means it's an f/4 (who cares? but these are interesting facts when we discuss telescopes more fully.)

The aperture specification is very meaningful but indirectly, because the aperture divided by the magnification gives the "exit pupil" diameter: 35mm aperture divided by 7 power = 5mm exit pupil. A 7x50 binocular has a 7.1 mm exit pupil. So what? Well, while f/# gives a relative measure of image brightness for a camera, the exit pupil compared to your own eye's pupil, determines the image brightness in binoculars. The exit pupil is the little circle of light you see when you hold the binocular away from your eye. The circle is actually the image of the objective, that is formed by the eyepiece.

1. Pupil Size

No, we're not in the school nurse's office! The human eye pupil is 2 to 3mm in diameter in daylight and goes up to 7mm at night when the eye is dark adapted. If the binocular exit pupil is at least as large as your pupil, the image will be about as bright as a normal view. If smaller, then the brightness is diminished by the ratio (there I go again) of the area of the exit pupil to that of the eye. A 7 x35 binocular will be just as bright as a 7 x50 in the daylight when your eye pupil is smaller than 5mm, but at night, the 7x50 will appear (50/35) squared = twice as bright!

2. Field of View

Another binocular specification describes how much field you actually see. More complex eyepieces allow a greater area of image to be seen, almost like a camera using a bigger piece of film. For example, a simple eyepiece will show 390 ft. at 1000 yards, while a more complex one might reveal 496 ft. at 1000 yards, under the same magnification.

Beware though. The larger field usually shows fuzzier images toward the edge. For viewing astronomical subjects, the field size can hardly be measured at 1000 yards, so we have to convert the specs to true field angles: 390 ft. at 1000 yards equals 7 degrees. That's the true field. Since the binocular magnifies 7 times, the field appears about 50 degrees in the eyepiece. The larger field eyepiece produces an apparent field of 65 degrees in the eyepiece: Every eyepiece has its own fixed apparent field.

The relationship between the apparent field of view and true field of view is only approximately proportional to the magnification. See the detailed discussion under Eyepiece Types.

We can see that a binocular has magnification, aperture, an exit pupil, a real field of view and an apparent field, all interrelated mathematically.

The Telescope

What does a telescope have that half a binocular doesn't: Flexibility - with interchangeable eyepieces with different focal lengths so almost any power can be obtained. Brightness: while most consumer binoculars have between 1 and 2 inches aperture, telescopes have 3, 4, 5, 6, 8, 10 or more inches aperture, so there's ample exit pupil for bright images at higher powers. Resolution: higher power, up to a point, shows greater detail. Detail is limited by the quality of manufacture, aperture, and turbulence in our atmosphere. In practice, about 50 power per inch of aperture is the upper practical limit.

For telescopes larger than 4 inches, the atmosphere generally limits detail, so powers above 200 or 300 largely magnify the turbulent fuzzy images. So why have large aperture telescopes? Because the "light bucket" capability shows stars vastly brighter and more numerous. Serious amateur astronomers and astrophotographers are usually aperture hungry to see faint galaxies, gas clouds and star clusters. For the less dedicated or beginning crowd, a small scope, up to about 5 inches, will show the rings of Saturn, belts of Jupiter, lunar craters and many "double stars" extremely well.

Unfortunately, many small telescopes are mere toys, but are promoted as high power instruments. A 250 power telescope with a 2" (50mm) diameter lens, on a flimsy mount is guaranteed to frustrate the beginner.

Since the magnification is given by the objective focal length divided by the eyepiece focal length, the longest focal length eyepiece possible will give the lowest power, largest exit pupil and brightest image for use as a spotting scope. The lowest useful power is about 4x per inch of telescope aperture.

Eyepiece Types

In general, telescopes with fast (f/4 to f/6) objectives require more sophisticated eyepieces for sharp imaging, particularly at the edge of the field. Modern multi-coated eyepieces come in a wide range of focal lengths. The best eyepieces have at least 4 elements. Plössl types are excellent for apparent fields up to 50 degrees, while more complex types have fields of 65 degrees, or even 80 degrees apparent field. The widest apparent fields offer eye-opening " spacewalk" viewing, whether of the Moon at high power or Milky way vistas at low power. In general, if an eyepiece with a wider apparent field of view is equally sharp compared to a narrow field, you have several potential benefits in performance (neglecting size, cost and weight). Let's compare, as an example, equally sharp eyepieces of 50° apparent field of view and 100° apparent field of view. If they have the same focal lengths, you will have the same magnification, exit pupil, but the 100° eyepiece will likely show you twice the true field of view (4x the field area) useful for larger astronomical subjects. However, you can also compare a 100° eyepiece with ½ the focal length of a 50° for getting the same true field of view in the sky. Now with the 100° you have twice the power, for more resolution, with half the exit pupil. This gives 4x darker sky background which allows fainter stars to be seen because of the greater contrast with the fixed brightness of stars. Unless the power is so high that the background becomes black, you will even see deep sky objects better, because the subject and background dim equally as the power goes up, maintaining the contrast, while benefitting from the greater resolution. The smaller exit pupil also minimizes the effects of eyesight aberrations and secondary mirror shadows in reflectors.

There are 2 standard eyepiece diameters common today; 1.25" O.D. and 2" O.D. There's much more variety and quality in the universally accepted 1.25" standard size. Many larger or more advanced instruments accept 2" O.D. eyepieces for the very largest field possible. Of course, smaller eyepiece sizes can be adapted to larger, but not the other way around.

Telescope Types
1. Refractor

With a long tube and objective lens up front, the refractor is and" looks" like a traditional telescope. It generally never needs alignment and usually has fine resolution. Typical amateur sizes are 2.4", 3" and 4" aperture. Below 2.4" you're better off with binoculars or a spotting scope. Because refractors usually are designed for f/12 - f/15, they can get rather large and expensive for the amount of light gathered.

I strongly recommend having one low power eyepiece with the widest apparent field in a focal length of 20mm or longer to avoid frustration when using refractors. An equatorial type mount is highly recommended, especially for 3" or larger aperture scopes used for astronomy. APO refractor designs from f/5 to f/8 are more portable, have wide fields and are simple to use. These "APO" types use special glasses to eliminate the color fringing seen with refractor models that use ordinary glass.

2. Reflector

Often called" Newtonians" after the inventor, Isaac Newton, these instruments use a concave mirror at the bottom of the tube to focus the light cone. A small flat mirror at the top reflects the light to the side where the image is viewed with the eyepiece. The 200 inch mirror telescope at Mt. Palomar is a Newtonian reflector.

A 6" Newtonian compares in size and cost to a 3" refractor, while an 8" compares to a 4 inch. You're gaining about four times the light gathering power but must contend with alignment adjustments and occasional cleaning of the mirrors in the open tube. f/5 models offer wider fields and are more compact than f/8 models which usually have slightly better image quality.

2. Catadioptrics

These modern instruments combine lenses and mirrors to make a very versatile, compact telescope. More expensive than equivalent size reflectors, they are called "Schmidt-Cassegrains", or" Maksutov" types depending on the nature of the correcting lens.

They're great for travel, and relatively light weight. Like refractors, their closed tubes keep optics clean and prevent air currents in the tube, which sometimes disturb images in reflectors. While most are in the f/10 to f/15 range, photographic versions are produced as fast as f/5.6. When a catadioptric is made this fast, the secondary mirror must be rather large which results in a large black spot in the middle of the exit pupil.

This causes some resolution problems at high powers and annoying shadows at very low powers. So consider these f/5.6 models primarily telephoto lenses, with moderate effectiveness as a telescope.

"Rich Field" Telescopes

Most scopes in the f/4 to f/6 range can be classified as "Rich Field", which means their power is low enough, field wide enough and exit pupil large enough to see wide areas of the Milky Way, with literally thousands of stars in view. Of course, this makes the scope ideal for spotting and photography if 35mm adapters are available.

The very best " Rich Field Telescopes" (RFTs) should be capable of using 2" type eyepieces for the widest field.

RFTs are made as refractors, Schmidt-Newtonians, " Newtonian" reflectors, and" Dobsonians" (John Dobson, a west coast amateur pioneered a style of Newtonian on a simple wooden alt. azimuth mount-like a gun turret). Most RFTs are not quite as good for high power, high resolution planet viewing as f/8 or longer telescopes. However "APO" refractors as fast as f/5 can be as good at high power as other type instruments.

Telescope Optics Showing Light Paths for Center of Field
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Telescope Optics Showing Light Paths for Edge of Field
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