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05-02-2011, 07:52 PM   #1
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Magnification and Macro Ratio

Hello everyone, it's my first post in Pentax community as I'm whilling to buy a K-5 and I'm also very new to Macro, so please, develop your explanations as would speak for a begginner.

After few hours of google researches I still can't find the right formula to calculate the Max Magnification factor. Here's the thing:

I dont know whether it makes difference or not, but this lens will be used into a K-5, which has a APSC sensor size. So I want to know how can I discover the Magnification Ratio of a given lens (e.g. Sigma 10-20mm F3.5 EX DC HSM which has a Minimum Focal Lenght of 16cm) ?

(I'm also missing the Min. Aperture of that lens).

Thanks again in advance for your time.

EDIT: Thanks for answering my first question audiobomber and Marc Sabatella.

EDIT 2: I've got the answers I was looking for, thanks everyone. =D


Last edited by Thales454; 05-03-2011 at 04:35 PM.
05-02-2011, 08:45 PM   #2
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Magnification and macro are inverses of one another. For the 10-17mm, 1/0.39 = 2.56, so the macro ratio is 1:2.6.

The Sigma at 1:5 would translate to 0.2X magnification, about half the fisheye's.

You can use a ruler to figure out magnification. A 1:1 macro lens will produce a photo with about an inch of the ruler filling the frame. The 10-17 will show about 2-1/2" at closest focus distance. The Sigma will show about 5" at minimum focus.
05-02-2011, 08:53 PM   #3
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Remember, a ratio is just a fraction. 1:2.4 means 1/2.5, which is 0.40. So the two different sites are basically saying the same thing. Meaning, at maximum zoom and minimum focus distance, you'd get that magnification. This is barely better than the kit lens, which does 1:3 or 0.33. The Sigma you mention does 1:5, which is 0.20 - noticeably not as good.

This is kind of splitting hairs, though. None of these qualify as macro lenses; they don''t even get you into 1:2 "sort of getting close to macro" territory. If you're truly interested in macro, you wouldn't be looking at any of these. You'd be starting at 1:2 (0.50) and up. And mostly, you'd be talking about primes. Or, you'd get a Raynox 150 to put in front of an ordinary telephoto zoom (see the Raynox Club thread).
05-02-2011, 10:58 PM   #4
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QuoteOriginally posted by Marc Sabatella Quote
Remember, a ratio is just a fraction. 1:2.4 means 1/2.5, which is 0.40. So the two different sites are basically saying the same thing. Meaning, at maximum zoom and minimum focus distance, you'd get that magnification. This is barely better than the kit lens, which does 1:3 or 0.33. The Sigma you mention does 1:5, which is 0.20 - noticeably not as good.

This is kind of splitting hairs, though. None of these qualify as macro lenses; they don''t even get you into 1:2 "sort of getting close to macro" territory. If you're truly interested in macro, you wouldn't be looking at any of these. You'd be starting at 1:2 (0.50) and up. And mostly, you'd be talking about primes. Or, you'd get a Raynox 150 to put in front of an ordinary telephoto zoom (see the Raynox Club thread).
Yes yes, I'm not looking for a Macro lens, I rarely take macro photos, but I would like to know how to do that math to discover if a given lens MAY be used for macro, because I've read Fish-Eye does some fun looking macros, but of course, it is not a professional macro tool at all :P

05-03-2011, 05:54 AM   #5
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warning Math involves

you asked for math, here it is

just remember there are few measurement definitionss to consider, with a simple lens.

Focal length (Fl) = the distance from the focusing plane for a subject at infinity
Subject distance(Ds) = the distance from the subject to the lens
Image distance(Di) = the distance from the lens to the focus plane (when focused at infinity Image distance = focal length)
lens extension (Le) = the distance the lens is extended forward (i.e. further away from the focusing plane) to focus at an object that is not at infinity. At infinity lens extension = 0


now for all lenses remember that when focused at any distance

1/Fl = 1/Ds +1/Di (you can see that at infinity the image distance is equal to the focal length)

You also need to consider that for a subject of height S the image height I is the ratio of Di/Ds = I/S, and I/S is the magnification ratio.

so now, if you want to add extension tubes to any lens,

1/Fl = 1/Ds +1/(Fl+Le)

or 1/Ds = 1/Fl +1/(Fl+Le)

this now gives you the working distance i.e. distance to subject(Ds) and if you consider the ratio of (Fl+Le)/Ds you get the magnification ratio of the lens (M).

You will get 1:1 Macro when Fl=Le and Ds=2Fl

Keep these formulas in mind and you can calculate your working distance and magnification ratio.

You can aslo consider adding diopters in front of a lens. the way a diopter lens works is the diopter number is 1/Fl, and by adding a diopter lens in front of any lens, the impact is that the infinity focus point is now the focal length of the diopter you add in front.

The lens focal length also changes, such that 1/Fl* = 1/Fl+diopter value where Fl* is the new focal length of the lens plus diopter, and the lens now has a permenant lens extension of Fl-Fl*

As a result, with the lens set at infinity the magnification ratio with a close up diopter lens is

M = Fl / (1/Diopter) where the Fl is the origonal lens focal length at infinity and 1/diopter is the working distance at infinity

Look at the formulas and you will see how simple it all is
05-03-2011, 07:07 AM   #6
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QuoteOriginally posted by Thales454 Quote
Yes yes, I'm not looking for a Macro lens, I rarely take macro photos, but I would like to know how to do that math to discover if a given lens MAY be used for macro, because I've read Fish-Eye does some fun looking macros, but of course, it is not a professional macro tool at all :P
Then I reiterate the recommendation for the Raynox 150, assuming you own a telephoto lens (zooms are particularly effective here). Best $40 you'll ever spend.
05-03-2011, 08:52 AM   #7
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QuoteOriginally posted by Lowell Goudge Quote
you asked for math, here it is

just remember there are few measurement definitionss to consider, with a simple lens.

Focal length (Fl) = the distance from the focusing plane for a subject at infinity
Subject distance(Ds) = the distance from the subject to the lens
Image distance(Di) = the distance from the lens to the focus plane (when focused at infinity Image distance = focal length)
lens extension (Le) = the distance the lens is extended forward (i.e. further away from the focusing plane) to focus at an object that is not at infinity. At infinity lens extension = 0

Look at the formulas and you will see how simple it all is
Yeah I'm familiar with some of these formulas, but what I still don't get is how the reviews get that magnification ratio, is there an ''avarage'' subject distance, so i can work around with that formula and reach some numbers or do they get as close as they can from the subject, which then would be Focal Lenght, but Image Distance will also be Fl if I set Focus at infinity... and... then I would have 3 Fls in the same equation? :x

O.o

(I think I missed something >.<)
05-03-2011, 09:15 AM   #8
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QuoteQuote:
but what I still don't get is how the reviews get that magnification ratio
Look at the specs of the lens?

E.g. 10-20mm F3.5 EX DC HSM - Wide Angle Zoom Lenses - SigmaPhoto.com specs 1:6.6

05-03-2011, 09:26 AM   #9
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QuoteOriginally posted by sterretje Quote
Look at the specs of the lens?

E.g. 10-20mm F3.5 EX DC HSM - Wide Angle Zoom Lenses - SigmaPhoto.com specs 1:6.6
There you go \o/

No more questions

I took a look in Amazon, but I think that was the wrong spot
05-03-2011, 10:36 AM   #10
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QuoteOriginally posted by Thales454 Quote
There you go \o/

No more questions

I took a look in Amazon, but I think that was the wrong spot
one thing to watch out for, is that the lens formulas are based upon what some call "working distance" i.e. the lens to subject distance, but many times in lens specifications, the minimum focusing distance is from the film/sensor plane to subject.

while in a lot of cases, the error introduced is minimal, i.e. who cares about a 50mm difference when shooting a person at 20-30 feet with your 50mm lens, but with macro, when working at 1-2 timess focal length, you are talking about a difference of 1/2 the total distance subject to focal plane.
05-03-2011, 01:10 PM   #11
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QuoteOriginally posted by Thales454 Quote
Yeah I'm familiar with some of these formulas, but what I still don't get is how the reviews get that magnification ratio, is there an ''avarage'' subject distance, so i can work around with that formula and reach some numbers or do they get as close as they can from the subject, which then would be Focal Lenght, but Image Distance will also be Fl if I set Focus at infinity... and... then I would have 3 Fls in the same equation? :x
Maximum magnification is always achieved at minimum focus distance. That's just common sense. Similarly, for a zoom, it will be at maximum focal length. Only possible exception would be a lens than can focus closer while not at maximum focal length than when at maximum lens, and then the maximum magnification might be achieved by finding the best compromise. Note, though, that many zooms don't really achieve their stated focal lengths at minimum focus distance - sometimes not even close. Focal length ranges are stated at infinity.

But I think you're making this way too complicated. You shouldn't need to calculate a thing. Maximum magnification is stated right in the specs. Either in ratio form (1:2.5) or decimal form (0.40), but it's the same thing either way. All lens specs list this figure, so no calculation should be necessary to understand what sort of macro capability a lens has. Might as well ask how to calculate, oh, I don't know, the maximum aperture of lens - it should be derivable from the focal length and front element diameter. But why bother when they tell you the maximum aperture right there in the specs?
05-03-2011, 01:23 PM   #12
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QuoteOriginally posted by Marc Sabatella Quote
But why bother when they tell you the maximum aperture right there in the specs?
Actually, I searched that lens spec in couple forums, but I didn't really went to Sigma's website as stated by sterretje above, but now I'm good
05-03-2011, 03:11 PM   #13
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QuoteOriginally posted by Marc Sabatella Quote
Maximum magnification is always achieved at minimum focus distance. That's just common sense. Similarly, for a zoom, it will be at maximum focal length. Only possible exception would be a lens than can focus closer while not at maximum focal length than when at maximum lens, and then the maximum magnification might be achieved by finding the best compromise. Note, though, that many zooms don't really achieve their stated focal lengths at minimum focus distance - sometimes not even close. Focal length ranges are stated at infinity.

But I think you're making this way too complicated. You shouldn't need to calculate a thing. Maximum magnification is stated right in the specs. Either in ratio form (1:2.5) or decimal form (0.40), but it's the same thing either way. All lens specs list this figure, so no calculation should be necessary to understand what sort of macro capability a lens has. Might as well ask how to calculate, oh, I don't know, the maximum aperture of lens - it should be derivable from the focal length and front element diameter. But why bother when they tell you the maximum aperture right there in the specs?
Marc

one real exception to the maximum magnification at maximum focal length for zooms is the version 1 vivitar Series 1 70-210F3.5. when put into the macro mode the lens changes significantly and becomes an internally focused 70mm lens using the zoom elements to focus, but that is a real exception, at least as far as I know, but I suspect that many zooms provide maximum magnification at all focal lengths and focus at different distances as a function of focal length.
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