What does the magnification number on binoculars and telescopes actually mean?
Asked 3/23/2017
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When binoculars are labeled 7x or 10x, does that magnification refer to linear size, area, or something else? I’ve seen statements like “10x makes an object appear 10 times closer,” but I’m unsure whether that means the object appears 10 times taller/wider, or whether magnification is sometimes quoted as area enlargement instead. Does the standard magnification used for binoculars, telescopes, loupes, and microscopes refer to linear magnification or area magnification?
Originally by Photography Stack Exchange contributor. Source · Licensed CC BY-SA 4.0
Photography Stack Exchange contributor
9y ago
2 Answers
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The magnification number of binoculars is the focal length of the objective lens divided by the focal length of the eyepiece lens (used to magnify the objective image).
http://en.wikipedia.org/wiki/Binoculars#Optical_parameters
This is exactly the same concept as telescope "power", and is extremely common knowledge among telescope users (who use several eyepiece lenses to vary power), but it is not very useful to binocular users to know. Nevertheless, it is.
It does not compare to camera lenses which are used at prime focus (no magnifying eyepiece lens).
It is said that the binocular power number compares to the naked eye, that 7x power is 7 times larger than the eye sees, as if it were 7 times closer. I cannot derive that definition.
Originally by user38978. Source · Licensed CC BY-SA 4.0
user38978
9y ago
0
Generated from our catalog & community — verify before relying on it.
For binoculars and telescopes, the quoted magnification is linear/angular magnification, not area magnification.
A 10x binocular makes an object’s apparent angular size about 10 times larger in each dimension, so it looks roughly as if it were 10 times closer. In that sense, something that appears 1 unit tall to the eye would appear 10 units tall through 10x binoculars.
Because both width and height are enlarged by the same factor, the apparent area would grow by the square of that factor. So 10x magnification corresponds to about 100x apparent area, not 10x area.
For binoculars specifically, the magnification is commonly given by:
magnification = objective focal length / eyepiece focal length
This is the same basic idea used for telescopes.
So if you’re choosing between “length vs area,” the standard magnification number refers to linear/angular enlargement. Area scaling is just a consequence of that.
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