Darkroom Digest: How I Calculate Bellows Factors & Magnification Ratios

October 02, 2016  •  2 Comments

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One of the reasons, among many, that I love large format view cameras is the ability to use a single lens for regular and closeup photography.  I use my standard or slightly wide-angle lenses for landscapes (120mm, 150mm, 180mm) and if I come across a beautiful flower during my hikes, I can use the same lens.  All I need to do is extend the bellows on my camera and figure out how much more exposure I need with the extra bellows extension.  I do a lot of flower photography, so I like to know the magnification ratios that I can achieve also.  All you need to know is the focal length of the lens, the maximum bellows extension of your camera, and the reciprocity failure of your film that you are using.  

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QUICK START INFO

I keep a journal with me when I am photographing and I have a few key pieces of information with me at all times.  One of those pieces of information is the bellows factor and magnification information for my lenses.  

For 1 to 1 (1:1) magnification for any lens, your bellows draw will be twice the focal length and the exposure compensation for this will be 2 stops.

For 2 to 1 (2:1) magnification for any lens, your bellows draw will be three times the focal length and the exposure compensation for this will be 3 stops.

For example, let's assume I want to use my 180mm Nikkor lens on my 4x5 view camera for some 1:1 close-up flower photos.  I know my bellows extension will need to be 2X 180mm (360mm) and my exposure will be 2 additional stops plus what I metered, plus any filters.  I will then apply reciprocity failure times for my film.  

New exposure = base exposure x exposure compensation factor + filter compensation and then a correction for reciprocity if applicable. 

My Chamonix 4x5 camera comes standard with 395mm of bellows draw and I have an extension board to take it to 480mm.  This means I can use my 120, 150, and 180mm lenses for closeup work with my standard camera.  If I wanted to use a longer lens like my 210mm, I could do that with my extension board installed.  

I have included two additional magnifications for you below:

0.75 - bellows draw is 1.75 x focal length of your lens and exposure compensation is 3X or 1.5 additional stops.  

0.4 - bellows draw is 1.4 x focal length of your lens and exposure compensation is 2X or 1 additional stop.   

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NEAR FOCUS LIMIT

When working with flowers and small subjects in nature, I like to know how close I can get to my subject before I make my lens selection.  I will give you the formula to make this calculation.  

F = focal length, D = minimum distance to subject from lens, B = bellows draw on your camera 

For example, if I wanted to use my 180mm Nikkor lens that I discussed in the quick start section above for a 1:1 magnification of a flower (360mm bellows draw), I would simply do the following calculation to determine my minimum focus distance: 

1/F = 1/D + 1/B

1/180mm = 1/D + 1/360

Using basic algebra we can solve for the third variable when we know the other two.  

To solve for 1/D we take focal length minus our bellows draw

1/D = 1/180 - 1/360

Now I convert the fractions to decimals 

1/D = .0056 - .0028 (.0028)

Next, I solve for the final step by dividing1 by .0028 by for a minimum focus distance of approximately 357mm (14 inches) 

CALCULATING BELLOWS EXTENSION FOR A GIVEN MAGNIFICATION

There are times when I want a greater magnification than 1:1.  I will first see if my desired lens will give me the magnification that I am seeking with my camera on hand before using a diopter.  If we stay with the same 180mm Nikkor lens in the above examples and I want a 2:1 magnification (2X size), how much bellows extension will I need for this scenario? 

Using the following formula, you can figure out the required bellows exertion for any lens and camera combination. 

M = magnification ratio, B = bellows extension, F = focal length of lens.

M = (B-F) / F

In our example, we want a 2:1 magnification using our 180mm Nikkor on our camera 4x5 view camera that has a maximum bellows draw of 480mm.  

M = 2/1, F = 180 B = ?

2/1 = (B -180) / 180

Using basic algebra, we can solve for the equation. 

(2/1 * 180) = B -180

360 = B - 180

To solve for B, we simply add 360 + 180

Bellows extension required = 540mm

In my case, I don't have enough bellows extension available on my camera to achieve 2:1 magnification using my 180mm lens.  If I really wanted to use this lens and this magnification ratio, I would use my diopter.

I have a 120 lens that I could use to achieve 2:1 magnification with a required bellows extension of 360mm.  

Tip: I do a mental shortcut to perform the above calculation.  It will take me longer to explain it to you then it does in real life.  For any given focal length, I double it (120 x 2) = 240, and then I add the focal length to that result (+ 120) and this result is my required bellows extension (240 + 120) = 360mm. For my 150mm lens, it would be 450mm.  An even faster shortcut is to triple the focal length for 2X magnification (120mm x 3 = 360mm bellows extension for 2:1 magnification). 

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CALCULATING EXPOSURE TIME FOR BELLOWS DRAW

In the above example, I wanted to achieve 2:1 (2X) magnification.  Using my 150mm lens, I determined that I would need 450mm of bellows extension.  The last piece of the puzzle after determining the magnification ratio and lens to use is to calculate your exposure time required for the extra bellows extension. 

New exposure = base exposure x exposure compensation factor + filter compensation and then a correction for reciprocity if applicable. 

Scenario: 150mm lens, 450mm of bellows extension, and a 2 second metered exposure

B = bellows, F = focal length 

Compensation = (B / F) squared 

Compensation = (450 / 150) squared or 3^2

Exposure Factor = 3 x 3 or 9 seconds exposure factor (3 stops)

New exposure time = 9 (compensation factor) x 2 (base exposure) = 18 seconds 

Note: based on the film you are using, now look up the reciprocity failure for 18 seconds and adjust as needed.

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Comments

Tim Layton Fine Art
Hi Jim, thanks for your comment and question. Absolutely feel free to print and put in your pack. Thanks a lot for even asking... not the norm any more unfortunately. Stay in touch.

Tim
Jim Spinoso(non-registered)
This is great stuff. Useful and practical information - is it OK to copy this post and keep it in my Arca Swiss 4 by 5 camera pack?
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