The physics behind telescopes – Rudiments of Telescopes

As mentioned before, choosing a good telescope is important in order to get started on stargazing. And, in order to choose one, it is pertinent that we study the fundamentals of a telescope. Then we will see the different types of telescopes. Well, to begin with, binocular is not a bad option. Although I haven’t personally used one for stargazing, experts say that you would be amazed at how useful binoculars are, even when it comes to stargazing and not just peeping into your neighbor’s house (well, let’s not get into that and just enjoy stargazing!). I will leave out the discussion of binoculars from this post, just to focus on what is more useful for astronomy – telescopes.

When we think of a telescope, what usually comes to mind is a long, slender, lightweight tube with lenses at the two ends. Something like this!

telescope-clipart-telescope

Well, although in a similar shape, the modern telescopes, used for astronomical viewing (solar system objects, deep sky objects like nebulae, in detail), come in a variety of sizes, composition and weights (some would even require a crane to be lifted). The old, historic telescopes, that you might see in observatories, are the size of a room.

tele_zeisscol

Above, the historic Zeiss telescope at the Griffith Observatory, Los Angeles. An interesting fact – More people have looked through this Zeiss telescope than any telescope in human history.

Technology has evolved, making telescopes compacter, although some physical limitations still stymie the further diminution of size.

Below is a modern telescope that is used as an alternative to the historic Zeiss telescope at Griffith Observatory for public viewing. And, you will be amazed to know that both of them show somewhat similar images (mostly in terms of magnification).

lawn_telescopesajc_700PXLS

One major factor leading to such gigantic sizes and bulk is aperture, technically defined as the diameter of the objective lens or mirror (remember objective from the previous post?).

Aperture

In optics, in general, an Aperture is a hole or an opening through which light travels. The aperture determines how collimated (parallel) the admitted rays are, which is of great importance for the appearance at the image plane. If an aperture is narrow, then highly collimated rays are admitted, resulting in a sharp focus at the image plane. If an aperture is wide, then uncollimated rays are admitted, resulting in a sharp focus only for rays with a certain focal length (distance traveled by the light ray). This means that a wide aperture results in an image that is sharp for things at a certain distance.[1]

The aperture also determines how many of the incoming rays are actually admitted and thus how much light reaches the image plane (the narrower the aperture, the darker the image for a given exposure time). Seems familiar? In the human eye, the pupil is the aperture. In telescopes, as noted before, aperture is not a physical hole but the diameter of the objective. If the objective is a lens, we can, in fact consider the entire lens as a highly thin ring where the inside of the ring is a transparent material made of glass rather than air. Now, the considering the analogy to a hole, the inside of the ring is a hole in the circular plate from which the ring was carved. The circumference of the ring is, technically, called aperture-stop.

This property of aperture that is indicative of the brightness of the image is most relevant to telescopes. Why is that important? As you know, the majority of the celestial objects seem faint (due to their distance to us). So, if we want these objects to appear brighter, we would need a higher aperture.

We will get into more details on aperture when we discuss the design of telescopes, but first take a look at another very important measure, the Magnification. Well, when we think of buying a telescope, we always think of getting the one that has the highest magnification. Some telescopes are advertized with over 800x zoom. Those are the telescopes that are sham. Never go for a telescope that is advertized like that. They are just playing with the human psychology that makes us think that “all we need in a telescope is magnification that is as high as possible“. Don’t feel offended if you were under that impression because I was no exception until I heard the truth from the experts. According to experts, 50x magnification per inch of aperture is usually the maximum beyond which there is hardly any more detail that you can see in celestial objects.

Before we go into the design of telescopes, let’s understand what we really mean by magnification.


Magnification

Magnification is the process of enlarging something only in appearance, not in physical size. This enlargement is quantified by a calculated number also called “magnification“. When this number is less than one, it refers to a reduction in size, sometimes called “minification” or “de-magnification“.[2]

While what is defined above is the process, there is also a number, namesake, that is used to mathematically define the measure of enlargement.

Magnification as a number (or optical magnification) is defined as the ratio between the apparent size of an object (or its size in an image) and its true size, and thus it is a dimensionless number. There are two types of this measure.

Now, before we study the two types, let’s first refresh our knowledge of “real” and “virtual”. A real image is formed when the emergent rays physically converge at a point like in the case of converging (positive) lenses like biconvex. A virtual image is formed when the emergent rays diverge like in the case of diverging (or negative) lenses like biconcave. These diverged rays, however, appear to be emanating from the other side (converging in the opposite direction) where the image is formed (called virtual because the rays just appear to converge at a point). Now, in case of modern telescopes and other instruments that make use of the eyepiece, the eyepiece, in order to keep your eyes relaxed and reduce strain, presents the image that appears to be at infinity. Now, because the image appears to be formed behind the eyepiece (the side from where the rays are emergent), the image is virtual.[3]

Linear (or Transverse) Magnification – For real images, such as images projected on a screen, size means a linear dimension (measured, for example, in millimeters or inches) .[4]

Screen Shot 2016-03-03 at 7.19.50 PM

where lo is the linear size of the object and li is the linear size of the image.

Angular magnification – For optical instruments with an eyepiece (like telescopes), the linear dimension of the image seen in the eyepiece (virtual image in infinite distance) cannot be given, thus size means the angle subtended by the object at the focal point (angular size). The angular magnification is given by:

\mathrm{MA}=\frac{\tan \varepsilon}{\tan \varepsilon_0}
where {\varepsilon_0} is the angle subtended by the object at the front focal point of the objective and {\varepsilon} is the angle subtended by the image at the rear focal point of the eyepiece.

For example, the angular size (the angular diameter or apparent size is an angular measurement describing how large a sphere or circle appears from a given point of view) of the full moon is 0.5°. In telescopes, with 200x magnification it appears to subtend an angle of 100°.[5]

After making some substitutions in the above equation for a telescope, this number can be simply defined as

Screen Shot 2016-03-05 at 10.30.47 AM

where fo is the focal length of the objective and fe is the focal length of the eyepiece.

Optical magnification is sometimes referred to as “power” (something that you would come across quite often when dealing with telescopes, for example “10× power”). As can be seen, focal lengths of the objective and eyepiece impact the power of magnification. For the same focal length of the eyepiece, higher the focal length of the objective, higher is the power. Similarly, for the same focal length of the objective, lower is the focal length of the eyepiece, higher is the power. Also, it is very useful to note that lower magnification means wider field of view. That’s something to consider when you want to look at a nebula or galaxy rather than the moon. So, highest magnification power is not always the need of the hour.


Focal ratio

Focal ratio (popularly known as f-number and sometimes called f-ratio, f-stop, or relative aperture) of a lens is defined as the ratio of the lens’s focal length to the diameter of the entrance pupil (effective aperture, the optical image of the aperture-stop, with diameter close but not equal to the diameter of the lens or aperture-stop). Like optical magnification, it is a dimensionless number. It is also a quantitative measure of lens speed (described below), and an important concept in photography (and astrophotography). The number is commonly notated using a hooked f, i.e. f/N, where N is the f-number.[6]

Screen Shot 2016-03-03 at 3.33.46 PM

where f is the focal length of the lens, and D is the diameter of the entrance pupil (effective aperture) of the lens. It is customary to write f-numbers preceded by f/, which forms a mathematical expression of the entrance pupil diameter in terms of f and N.[2] For example, if a lens’s focal length is 10 mm and its entrance pupil diameter is 5 mm, the f-number is 2, expressed by writing “f/2”, and the aperture diameter is equal to f/2, where f is the focal length.

Ignoring differences in light transmission efficiency, a lens with a greater f-number produces darker images. Doing some math, keeping the focal length of the lens fixed, larger the effective aperture, smaller will be the f-number. This indicates that for the same focal length, smaller f-number means more light is captured by the lens (bigger aperture) and thus brighter will be the image. Conversely, for the same focal length, higher f-number means darker images are produced. Now, keeping the aperture fixed in the equation and just varying the focal length, it can be seen that higher focal length means higher f-number and darker images, and conversely, brighter images with smaller focal length (smaller f-number). We can, thus, see how this number is so important to telescopes.

A related concept called Lens speed, mentioned above, is relevant to photography (and astrophotography). This measure refers to the maximum aperture diameter, or minimum f-number, of a photographic lens. A lens with a larger maximum aperture (that is, a smaller minimum f-number) is called a “fast lens” because it delivers more light intensity (illuminance), achieving the same exposure with a faster shutter speed (the length of time when the film or digital sensor inside the camera is exposed to light, also when a camera’s shutter is open when taking a photograph). A smaller maximum aperture (larger minimum f-number) is “slow” because it delivers less light intensity and requires a slower shutter speed.[7]

Trust me, these properties will help you a great deal when it comes to choosing a telescope and its different accessories (discussed later). With these in mind, now let’s delve into the design of telescopes (primarily astronomical). Although the essence of all telescopes remains the same, there are different types of these telescopes, designed with primarily optical differences. In order to choose the best telescope, there are several factors to consider like what celestial objects  you want to gaze at, how big you want to see them, how portable you want the telescopes to be. With one telescope, in order to achieve one goal, you might have to compromise on the other. Even money cannot buy a telescope that gives you everything (at least not yet). However, what money can buy is more than one telescopes in which case you can achieve everything (although, probably, still not how you would like it).


Telescopes, like everything else in this world, come in different flavors. There are, primarily, three kinds of telescopes: Refracting, Reflecting and Catadioptric. We will study each one in the subsequent posts.

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