I am in the market for either a telescope or binoculars, however something puzzles me…
In my browsing, I have found many different magnification powers, 7x, 8x, 10x, 20x and so on.
I fully understand the x-factor in the sense that if you are using e.g. a 10x lens, the thing you are viewing appears ten times closer, than in view of the naked eye.
What I do NOT understand is, the math involved in the x-factor. If what I am viewing is 500 feet away, and I am viewing it with a 10x lens, then how close is the image, appearing in feet??? In other words, if I am looking a tree 500 feet away, with a 10x lens, how many feet “closer” would I seem be to the tree?
Please explain the formula/process for making this type of calculation, also.
Pardon my over-explanation, but I wanted to make sure I was clearly stating my question.
I once saw a telescope so powerful that it would bring objects up so close sometimes they would appear to be behind you.
>> I fully understand the x-factor in the sense that if you are using e.g. a 10x lens, the thing you are viewing appears ten times closer, than in view of the naked eye.
Well, you have just given yourself away. You don’t understand it. When a telescope is 10x it does not mean it brings anything closer. You’d need a truck for that. What it means is that it magnifies the angular diameter by a factor of 10. If a distant object subtends an angle of 1’ then, when viewed through that instrument it would subtend an angle of 10’. For very small angles (which is always the case) this is the same as if the object were ten times bigger in diameter.
I have seen the practice with microscopes of referring to are magnification rather than diameter. The are is the square of the diameter and so you get huge numbers which sound more impressive. But with telescopes it’s always the diameter.
One thing though… [B} DON’T EVER [/B} buy a telescope advertised primarily by magnification. This is invariably the hallmark of a cheapo telescope. Good ones are sold based on aperture- in millimeters for refractors, and inches for reflectors. This makes more sense, when you consider that light gathering is the important factor for a telescope. Bigger means brighter, and you can always change your eyepieces for different magnifications & fields of view.
Really, same goes for binoculars, except that exit pupil is an important consideration- anything over 5mm is way overkill in daylight(exit pupil = objective lens / magnification)
Coatings & prisms are very important to binocular clarity. You want fully multi coated surfaces(all air-glass surfaces fully multicoated), and Barium crown glass prisms with total internal reflection(BAK-4) instead of borosilicate (BK-7).
I have a pair of Orion 8x56, and it’s stunning how much better they are than my cheap-ass Tascos, but they only cost about twice as much.
Just remember that the best first telescope is a pair of binoculars!
They’re easy to use, light and portable (and thus will be used)
They give an upright, left-right preserved image
If you give up on stargazing, they’re still great for sports, bird-watching, …
For the same dollar amount, a pair of binoculars is always of much better quality than its equal-priced telescope counterpart.
For binoculars, the first number is the magification and the second number is the diameter of the objective lens in mm. So, a 10X50 pair will magnify by ten times and each part will have a fifty millimeter diameter. The ratio of the diameter to the magnification yields the so-called ‘exit pupil’ in mm. In the case of 10X50 binoculars, it’d be 5 mm. Most people over the age of 40 or so can’t dilate their pupil to much more than that. So, for them, getting, say, a 11X80 pair, with an exit pupil of over 7 mm simply wastes light - their pupil is too small to accept it.
Whatever you do, never buy a telescope from a department store or mall photo-developing shop. Never. Its quality will be very poor. And, as mentioned, never buy a telescope where the manufacturer or seller makes a big deal about how much it magnifies. It is a lie.
I’m not disagreeing with sailor, but an object 500 feet away viewed in 10x magnification would look about the same (subtend the same angle) as if you were about 50 feet away without magnification.
That’s one way of looking at the way telescopes distort perception. An object 600 feet away would look the same as if you were 60 feet away–in other words, even though they’re one hundred feet apart, they’d look like they were ten feet apart. The field of view gets flattened.
In case Sailor didn’t make it completely clear for you MSK, an object under 10x magnification will appear to be about 50 feet away if it is actually 500 feet for objects that subtend small angles, which are most object since telescopes and binoculars have small fields of vision.
The math involved is trigonometry. I’m not sure how to explain it with out using the same words as Sailor, but I’ll try. Objects appear large or small, and therefore far or near, because they take up angular sections of our field of vision by different amounts. Lets say you are far enough away from a tree that you see the top and the bottem at once. If you draw a line between the top of the tree and your eye, and then draw another line from the bottom of the and your eye, there will be an angle between them at your eye. This is the angular height of the tree. If you move closer, this angle will get bigger, farther it will get smaller. This difference in angle, plus your general knowledge of how big the tree actually is, lets you estimate your distance from it.
You wanted the math, so their it be.
Now if you look at that tree under 10x magnification the naked eye angle height will be multiplied by 10. It will make it appear that the object is only one tenth the distance away, if the angle is small. This is because sin x=x approximatly for small x (sorry I don’t know how to do approximately equals to). I could probably give you a BS answer why this is true, but I really don’t know. If the angle is not small then some more trigonometry is required.
>> I’m not disagreeing with sailor, but an object 500 feet away viewed in 10x magnification would look about the same (subtend the same angle) as if you were about 50 feet away without magnification.
Well, not really. Initially it may seem like the the same thing to say an object a 1,000 feet away seen with 10x appears to be ten times larger at the same distance or the same size and ten times closer. But the first statement is truer than the second because if it were ten times closer you’d gain stereo vision which you do not. To make it appear ten times closer you would have to separate the distance between your eyes by a factor of ten (which can be done with prisms). It is well known that objects seen trough binoculars appear flat for this reason. In fact, they appear to be at the same distance and ten times larger. Even with a telescope this is noticeable.
>> But you could use binoculars with wider separation (most binoculars are wider–just not ten times wider) and the image would still be flat.
That’s my point. It does not appear to bring the object closer, it appears to make it larger at the same distance. To make it come closer you would have to multiply the distance between the eyes by the same amount as the magnification (again we are talking small angles). Then it would appear closer in that same proportion.
The main reason binoculars have prisms is to shorten them. The added width is very minor and only noticeable when viewing nearer objects.
Sailor: your statement that the flattening effect can be seen in a telescope makes no sense to me – in a monocular telescope, one’s only judge of distance is size, so everything looks flat in that sense.
Also, as to Dr. Lao’s mention of the small-angle approximation of the sine function: there’s a very good reason that sin x =~ x for small x. Any continuous function, including the sine function, can be expressed to arbitrary accuracy by a Taylor series – basically, you start with a point where the function and its derivatives are known, and you can multiply the derivatives by appropriate factors to build up a better and better facsimile of the original function. When this is done to a sine function, the result is: sin x = x - x^3/(3!) + x^5/ (5!) - x^7/(7!)+… As you can see, there are no odd-numbered terms, so the approximation sin x = x is correct to second order, and only breaks down when x^3 becomes significant.
Mrs. D just bought a pair of image stabilizing binos. Very sweet. Worth the $ IMO.
She also has a 3.5" refractor and an I don’t know how large Dobsonian. Me, I just look through them and see pretty things. And I’d much rather tote her binos than haul those scopes around.
>> Sailor: your statement that the flattening effect can be seen in a telescope makes no sense to me – in a monocular telescope, one’s only judge of distance is size, so everything looks flat in that sense.
Pault, if you read carefully i explained the issue with binocular vision and then added “Even with a telescope this is noticeable.”
What I meant is that it is not noticeable to the same degree. The noticeabilty is in proportion to the binocular separation. prismatic binoculars are better than plain eyesight, etc. But even a monocular telescope you are dealing with the small angle subtended by the diameter of the lens. While this is very small I believe it does give a small perception of depth (which would not exist if the lens had a tiny diameter).
My main point is that visually enlarging the object at the same distance and bringing it closer are not the same thing.
There is also another issue: the magnification is not an exact number. It depends on a number of things like the distance of the object and your own eyesight. I am nearsighted and I have to adjust the ocular lens accordingly and this gives me less magnification. But we are getting too technical here.
The main things to consider when buying binoculars or telescope are: Diameter of the objective lens (capacity to gather light in the dark), quality of the lenses, magnification. In the case of a telescope the mount is also very important. Azimutal is worthless for astro observations where you need polar mount.
Do you mean “Azimutal is worthless for astro observations where you need polar mount” or “Azimutal is worthless for astro observations, where you need polar mount.” The first is true, but the second is not. Large-aperture Dob owners do quite well with altazimuth mounts.
MSK, what do you want the scope for? Terrestrial, or astronomical? For terrestrial, magnification probably is more important than aperature, since you’ll be using it in plenty of light. You’ll also probably want something that produces upright images. For astronomical, aperature isn’t everything, but it’s awfully close.
As to polar vs. alt-az mounts: Polar with a clock drive is a must if you intend to do any photography, but for naked-eye and relatively low magnification, an undriven alt-az (such as the popular Dobsonian mount) will do just fine, for a fraction of the cost. For higher magnifications, objects will drift out of your field of view rather quickly without a drive, but there’s very few things in the sky that call for magnification.
If this is your first scope, you’re probably best off going with a pair of binocs. They’re easy to use, and you can use them for five minutes at a time, if you want (a mounted scope can take as much as a half-hour to set up and put away). I’d also recommend that you look up your local astronomy club (preferably, a group with affiliations with the Astronomical League), and see about joining. This’ll give you a lot of folks who’ll be glad to show you around the sky, and they’ll probably organize star parties periodically where you can all get away from the city lights and spend a few nights observing.
BTW, I failed to mention that I do not know diddly-squat about trigonometry. Unfortunately, the math and formulas are greek to me. I had hoped it would be simpler than that. I am not adept at mathmatics beyond the basics. Thank you for trying though. I do have some better understanding of how to properly select a pair of binocs now.
Not astronomy? Oh. In that case, ignore most of the advice you’ve gotten from this thread thus far.
You still shouldn’t be overly impressed by magnification, though. You can magnify an image pretty much as much as you want, but it won’t do you any good if you can’t see any additional detail that way. A more significant criterion is resolving power, which depends on the quality of the optics, among other things.
