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03-08-2008, 06:26 PM   #1
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How to do the math for a closeup lens?

Hi

I am currently investigating what is the closeup lens suitable to bring a normal lens close to 1:1 and after searching the forum, I came across this post:

QuoteQuote:
with a close up lens attached, you effectively change the focal length of your prime lens (i.e. you shorten it.

the effective focal length of the combination is

New focal length = (FL_old x FL_close_up) / (FL_old + FL_close_up)

FL_Close_up = 1 / diopter

Maximum Working distance becomes the focal length of the close up lens, since a 1 diopter lens has a focal length of 1000 mm (1 meter) the maximum working distance with a 1 dipoter lens is 1 meter.

so if you consider a 28 mm lens with a +1 diopter close up lens, at 1 meter distance you will have a magnification ration of 28/1000 or 1:40, but the same close up lens on a 100MM lens, at 1 meter gives you 1:10.

If you add a 5 diopter close up, your maximum focus distance with your 28mm lens will be 200mm therefore the magnification ratio will be 28/200 or about 1:7, but on the 100MM lens a +5 diopter at maximum distance will give you 1:2. (this is getting close to the 1:1 you want, and you now are working at 1 meter. you will have some ability to come inside this distance as a function of how close you lens focuses.

Okay. In my case, my lens is a 75mm with 1:3.9 magnification. So assuming I am using a +5 dipoter, the

FL_close_up = 1/5 = 200mm.

New focal length = (FL_old x FL_close_up) / (FL_old + FL_close_up)
= ( 75mm x 200mm ) / (75mm + 200mm)
= 54.54mm

What does this 54.54mm relating to? The "1:3.9" never come into place in the above equation.

So what would a +5 diopter bring the magnification of 1:3.9 to?

Thanks for any insights.

03-08-2008, 06:56 PM   #2
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QuoteOriginally posted by raider Quote
Hi

I am currently investigating what is the closeup lens suitable to bring a normal lens close to 1:1 and after searching the forum, I came across this post:
I think I recognize this as my scribblings so I will answer this. Note that I am currently working on a spread sheet to perform all these calculations, which I keep in my PDA,

QuoteQuote:


Okay. In my case, my lens is a 75mm with 1:3.9 magnification. So assuming I am using a +5 dipoter, the

FL_close_up = 1/5 = 200mm.

New focal length = (FL_old x FL_close_up) / (FL_old + FL_close_up)
= ( 75mm x 200mm ) / (75mm + 200mm)
= 54.54mm
ok, so far so good, you have established the new effective focal lenght.
QuoteQuote:

What does this 54.54mm relating to? The "1:3.9" never come into place in the above equation.
you've got it, the 1:3.9 is the maximum magnification ratio of the origonal lens at closest focus
QuoteQuote:
So what would a +5 diopter bring the magnification of 1:3.9 to?

Thanks for any insights.
go back to the concept that magnification ratio is the ratio of subject to lens distance over lens to film(or sensor) distance

you have made a new lens with a 54mm focal length, but which is 75mm from the sensor or film at infinity, and which at infinity focus can focus out to 200mm, therefore your new lens can go from 1:200/75 or 1:2.66 to something higher.

That something higher you need to calculate.

This needs more math, and some estimations about your lens.

I have not yet got all the formulas set up for this, so I have worked backwards with my current version of the spreadsheet, which i also use for calculating the benefits of extension tubes.

You lens, from the magnification ratio, can close focus to about 370mm from the front element, and to do so, effectively moves the front element out away from the film/sensor 19mm

When you consider the new focal length, with the 5 diopter close up, it is a 54mm lens, extended out 21mm at infinity. using this, and the lens extension to minim,um focus of 19mm for a total extension of 40 mm , I estimate your maximum magnification will be 1:1.5

You can get the formulas on Photography - Wikipedia, the free encyclopedia

As I said, this is a work in process so I don't have all of them yet in a simple form to post
03-08-2008, 07:44 PM   #3
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just use extension tubes, if you want 1:1(life size) with a 50mm lens you need 50mm of extension, for 1/2 life size use 25mm tube.
My first macro outfit was a 50mm F1.4 & 2 25mm ext tubes, some of the best macro shots I ever took was with that setup.
03-08-2008, 09:54 PM   #4
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One of the reasons I switched over to Pentax from Nikon was for this exact reason mostly for the bokea (please ecuse me I never spell this right). Especially in the 50mm range close up. I have found the the F50 1.7 to be somewhat the perfect lens for this without any enhancement of hardware extensions.

Could you please elaborate as to why extensions would make the process more exceptional?

03-08-2008, 10:10 PM   #5
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Thanks Lowell for the post.

A couple of questions if you don't mind:

Question 1:
How to you derive the focusing distance of 370mm from the magnification ration of 1:3.9?

Question 2:
Ok. You said that with the 5 diopter close up, the 75mm lens would become it is a 54mm lens, extended out 21mm at infinity.

I understand that this 21mm = focal length of old lens - new focal length of lens with diopter
= 75mm - 54mm.

But I don't get this: "using this, and the lens extension to minim,um focus of 19mm for a total extension of 40 mm , I estimate your maximum magnification will be 1:1.5"

How do you get the 1:1.5?

Question 3:
Putting a +5 diopter will make the 75mm lens become 1:1.5. So, in this case, does it matter if the lens in the first place can achieve 1:3.9 or 1:2 or whatever? The issue of original magnification would become immaterial in this case right?

Thanks!
03-09-2008, 06:04 AM   #6
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[QUOTE=raider;192148]Thanks Lowell for the post.

A couple of questions if you don't mind:

Question 1:
How to you derive the focusing distance of 370mm from the magnification ration of 1:3.9?
[/quote}

Basic optics, magnification ratio is the ratio of subject to lens distance over lens to image distance. If the magnification ratio is 3.9 that defines, it all, if focal length is known. if you do a search on lens calculations you will find the formulas
QuoteQuote:
Question 2:
Ok. You said that with the 5 diopter close up, the 75mm lens would become it is a 54mm lens, extended out 21mm at infinity.

I understand that this 21mm = focal length of old lens - new focal length of lens with diopter
= 75mm - 54mm.

But I don't get this: "using this, and the lens extension to minim,um focus of 19mm for a total extension of 40 mm , I estimate your maximum magnification will be 1:1.5"

How do you get the 1:1.5?
again, there is a set of equations that you can apply for the lenses and use of extension tubes. the 21mm is like an extension tube, also, as part of the calculation for magnification ratio you get the distance the lens moves away from the sensor (19mm in this case) as a result what you have is a 54mm lens extended away from the focusing plane by a total of 40 mm there is a calculation for this
QuoteQuote:
Question 3:
Putting a +5 diopter will make the 75mm lens become 1:1.5. So, in this case, does it matter if the lens in the first place can achieve 1:3.9 or 1:2 or whatever? The issue of original magnification would become immaterial in this case right?

Thanks!
Not quite the lens becomes a lens with a magnification ratio of 1:2.6 when focused at infinity, to 1:1.5 at minimum focus.

The initial magnification ratio is important because the closer it is to 1:1 implies the greater the range of movement in focusing, the close up lens and maximum focusing distance at infinity defined the 1:2.6 but the lens extension to give you minimum focusing distance of the lens on it's own (and hence the magnification ratio) define how much further out you can push the lens, to increase magnification,.

When I get all my calculations done, I will post them. As I said this is a work in process, and what I am doing is setting up a spread sheet with useful photographic calculations, which I carry in my PDA. I take that with me usually on trips, and it is useful to be able to look at these things from time to time. Of course, I could print this all out for each lens on the equivelent of a business card and laminate them, but if you consider 1 card per lens, with everything I have already, it is approaching the size of my PDA

the only importance the origonal
03-11-2008, 05:57 AM   #7
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Thanks for your reply. Appreciate your effort.
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