Which “photo equations” do you carry in your head? Do they interfere?

[Heroique]

Not everyone owns (or wants to carry) a tome full of photographic equations that might be useful only now and then in field or darkroom.

I’m curious if many here select a few equations (or mathematical principles) important enough to commit to memory – either for quick mental use, or working-out w/ pad & pencil, as the occasion warrants. Many of these principles likely deal with the behavior of light.

I’d suspect this selection would differ among studio, architecture & landscape people. And, I can only believe that the more pre-visualization one does, the more equations are made available for instant recall.

For example, the famous 1/u + 1/v = 1/f might be useful for careful photographers in the studio, but not as important for photographers of “sublime” landscapes. (For the curious: u=distance to subject; v=bellows extension; f=focal length.)

— What “math” (or principles) are useful for you to memorize and why?

— Can you recommend specific equations for certain types of work?

— When do you think this interferes w/ creativity, instinct, or intuition?

[Richard K.]

Well, there's the old bellows factor one:

Exposure increase factor= square of *extension÷square of focal length of lens

Thus working at 1:1, extension =2f and the factor becomes 4x or 2 stops.

*measured from lensboard plane to GG plane

There's also the imagining of the 3 planes required to render the Scheimpflug thingie...

[Dan Fromm]

I sometimes use flash. So, flashes are tested to get true ISO 100 feet guide numbers. In the field I use guide number arithmetic, adjusted for magnification, to find flash power setting and flash-to-subject distance to get the aperture I want to use. GN = f/# * distance. distance = GN/f/#. And so on. Read f/# as "f over number"

Relationship between magnification, lens' focal length, and extension. Rear node-to-film distance = f * (m + 1).

Relationship between magnification, aperture set, and effective aperture. EA = f/# * (m + 1). Note, this assumes a lens with pupillary magnification = 1. If PM is far from one this formula gives badly wrong advice.

Using these formulae is essential when working closeup, with one exception. The exception is a miraculous little flash bracket I built that gives correct exposure at the same aperture set from roughly 1:5 to 2:1. The flashes attach to the front of the lens and the gadget takes advantage of the facts that as magnification increases the distance from the front of the lens to the subject falls and as magnification increases the effective aperture gets smaller. With the right geometry the two effects offset each other nearly exactly over a useful range.

None of this interferes with instinct or intuition. Both are terrible guides when working with flash or closeup.

[Mark Sawyer]

Well, there's the old bellows factor one:

Exposure increase factor= square of *extension÷square of focal length of lens

Thus working at 1:1, extension =2f and the factor becomes 4x or 2 stops.

I know this is what every large format book quotes, but I never understood why people bother with it; "the square of this divided by the square of that gives you this exposure factor which converts to that many f/stops..."

Measure the focal length and aperture, divide, and you have your true f/stop. (And if you really want to be lazy, set your aperture at one inch. Twelve inches extension = f/12, twenty inches extension = f/20...)

[Helen Bach]

Measure the focal length...

Wouldn't it be better to write 'image distance' or somesuch rather than 'focal length*'? (Although folks will know exactly what you mean anyway.)

Best,
Helen

*the distance between the focal point or principal focus and the rear or second nodal point, the focal point being the point at which collimated light is brought to a focus.

[Jon Shiu]

For every 50% bellows extension greater than infinity focal length, add one stop exposure. So, for 8 inch lens focused with 12 inches of bellows extension, add one stop. 16 inches bellows extension, add 2 stops.

Jon

[Erik Larsen]

F=ma and my approximate terminal velocity of 120mph always seems to stick in my mind. It's always good to know how much force I will have when I fall off a cliff over hang and splat on the canyon floor below or it's nice trivia to guess how much force that precariously perched boulder 100 feet above me will have when it lets loose and takes me out:) other than that, sunny 16 is the only equation I can remember.
Regards
Erik

[Vaughn]

Light + film + printing process = photograph (sometimes)

I try to keep the price of film and the price of gasoline out of the equation.

[Heroique]

One type of photo math that still trips me is determining a filter’s effect on aperture vs. shutter speed – that is, translating between “stops” and “factors.” Especially when “stops” includes a fraction, like “1-1/3 stops.” For me, it can make trigonometry & calculus seem simple by comparison! So I carry filter specs for both, and even memorize a lot of it to concentrate better.

[Vaughn]

I don't even think of f stops and shutter speeds until I arrive at the amount of the exposure I want to give the negative. At that point I weigh the DoF I want against any shutter speed needs the image might have (then add what ever number of "stops" I need for any filter I might use.

I like my Pentax spot meter -- I read the darkest shadow I want detail -- say the meter gives me a "2" there -- so I plan my exposure at "4" ("2" will then be at Zone III). If I use a yellow filter (one stop), I change the exposure from "4" to "3". Then I set "3" on the dial and pick the f stop and shutter speed that suits best.

So much nicer working with plain numbers rather than counting up or down f stops and/or shutter speeds! No accidently skipping f/32 when counting 3 stops up from f/16 and things like that when I am tired or rushed!

[Andrew O'Neill]

Bellows extension. Easy to remember the formula, but forget about calculating in your head. Having a chart in my exposure record form helps big time.

[Emmanuel BIGLER]

Bellows extension.

Ext = M x F
Dist_from_lens_to_subject = (1 + 1/M) x F

but this more useful to chat on various LF forums and be the first to answer the F.A.Q : how much bellows draw do I need with my ... :D

[Bill_1856]

Well of course I always remember that the luminance of the moon is 250 c/square ft (or whatever).
It frequently helps when I'm drunk as a skunk and can't find my light meter.

[MumbleyJoe]

While I think I can remember the equations I opt to make cheatsheets that I keep in my little exposure notebook instead.

I only own 3 lenses (90, 150, 210mm) so I make tables that are more practical to carry around based on my own gear instead.

I just put together a table for 1/u+1/v=1/f. Basically, since my bellows is always somewhere between 90mm and 300mm (full extension of my bellows), I have one table that shows the focal distance for each of those 3 lenses in 1cm increments from 90-300mm. For as often as that's helpful in the field, I figure that's good enough.

Bellows | 90mm | 150mm | 210mm |
90mm | infinity | NA | NA |
100mm | 900mm | NA | NA |
110mm | 495mm | NA | NA |
...
150mm | 225mm | infinity | NA |
etc...

I also put together a table for bellows extension and effective f/stop in 1/3 stop increments, along with their corresponding exposure times (this was I always have a handy table that shows how 'stops' and 'exposure times' correlate). This was I can measure the bellows and figure out, within 1/3 of a stop, how to determine the effective f/stop (or exposure time).

f/stop | exposure | 90mm | 150mm | 210mm |
0 | 1x | @90mm | @150mm | @210mm |
1/3 | 1.3x | @101mm | @168mm | @236mm |
2/3 ....
1...
...

I also carry reciprocity tables for the films I use and some other cheat sheets.

I guess I could have just said I don't try to remember the equations in the field, but rather make sure I get it right when I've got the time and use cheat sheets when it counts.

[jnantz]

i don't carry any equations in my head
i just take the photograph ...

[aduncanson]

Sunny 16 is probably the one I most use. Others (like 1/f = 1/So + 1/Si) are firmly fixed in my head and I can't forget them even though I rarely use them while photographing. The two image conjugates, Si = f*(1+m) and So = f*(1 + 1/m), are highly for useful for closeup photography.

I often find myself re-deriving the relationship between aperture, subject distance, CoC, and depth of field so I cannot claim to carry that in my head, but Emanuel Bigluer's rule: "CoC = format diagonal/1780" is key.

One formula that I have recently developed with the intent to memorize is the following approximation for Ilford's published correction for HP5+ reciprocity failure:
t' = t^2/10 +2*t . It is accurate to within about 4% from 5 through 35 seconds.

[bob carnie]

Sunny f16
Fstop scale
shutter scale

[Heroique]

For reciprocity correction, it’s noteworthy that AA recommends the following corrections (from Kodak) for all b/w films, until you’re good enough to test the films you actually use. For intermediate times – such as “5 sec.” or “50 sec.” – simply interpolate, he says. (Note the “either/or” pairs for aperture/actual exposure are not always equivalent.)

Very simple – easy enough to memorize in a pinch :) :

Metered time / (either) new aperture / (or) actual exposure / development time
1 sec. / 1 stop more / 2 sec. / -10%
10 sec. / 2 stops more / 50 sec. / -20%
100 sec. / 3 stops more / 1,200 sec. / -30%

[Doremus Scudder]

No equations in my head. Not one. I don't want to be figuring mentally when photographing.

I carry a light meter to calculate exposure. I have made a guide book for myself with reciprocity tables for various films, bellows extension factors for all the lenses I own, exposure compensation for different developing schemes, filter "fudge-factors" (more later) etc. In short, if I need to calculate something in the field, I've done it already at home, with the calculator with significantly greater precision than I can in my head, and I just look it up (which likely takes less time than figuring in my head as well).

For filters, I read through them with my spot meter and then apply "fudge-factors" which I have determined through testing, and which compensate for small changes in contrast and exposure. These are only needed for the strongest filters and I usually have them in my head (#25 = +2/3 stop and N-1, for example). I also know my exposure compensation for N-2 through N+2. These can hardly be considered photo equations, however.

I'm fairly confident in calculating exposure, since I've tested everything. For that reason, I don't have to do a lot of figuring in the field. All the testing just so I can concentrate on the image and the adjustments to the focal plane and related camera movements (which requires some 3-D thinking) instead of doing the numbers on-site.

About reciprocity correction: every film is different. The Adam's "recommendations" are really the Kodak data for their older films. Howard Bond and others have tested the newer versions and have arrived at significantly different results (I posted just recently about this very thing). And, if your working E.I. is significantly different than the rated ISO, your reciprocity results may be way off. Get the data for the film you are using (Google is your friend here) and use that as a starting point, adjusting compensation time and developing time adjustments to get results you are happy with. Applying the old Kodak data is better than guessing, but not precise for many films today.

Best,

Doremus Scudder

[Heroique]

I don’t carry any equations in my head...


No equations in my head. Not one...

Perhaps a case of not meaning what one says? No one will convince me that you (you, of all people, Doremus ;) ) might come upon a situation where, say, “sunny-16” is best, then have to pull-out charts, tables or notes to recall the principle and use it.

Another “bellows correction” example (simple for the head, similar to John’s post #6) occurred to me, which some people recommend if your subject is closer than 10x your focal length (e.g., w/ a 240mm lens: 10 x 240mm = 2400mm, or closer than 2.4 meters).

If you’re closer, simply add ½ stop for every 25% increase in your bellows extension (beyond infinity).

[Kirk Gittings]

My kind of "equation"..........."The longer I fool with framing an image the more it sucks". Great images just grab me and almost frame themselves, as if I am more of a conduit than the creator.

[johnmsanderson]

My kind of "equation"..........."The longer I fool with framing an image the more it sucks". Great images just grab me and almost frame themselves, as if I am more of a conduit than the creator.

TRUTH.

[Drew Bedo]

Inverse square Law, but I rarely plug in values and work the numbers.

Usually I measure the film-to-flange distance. For my 150mm lens the correction is 1/3 stop per inch. for my 210mm it is 1/4 stop per inch.

[Jay DeFehr]

I'm sure a few equations, in some form, rattle around in the back of my head somewhere, but rarely rise to the level of consciousness. At some level, I estimate exposure based on the Sunny 16 rule/ experience, and make allowances for bellows extension; roughly 2 stops for head and shoulders portraits and 1 stop for 1/2 figure in 8x10, and rely on the latitude of my materials to compensate for any errors in my estimation.

[MIke Sherck]

"Is the subject close?" Add a stop.
"Is it really close?" Add another stop.

Don't interfere.

:)

Mike

[Two23]

$1,200 photo gear + 1 wife = trouble.



Kent in SD

[Doremus Scudder]

Heroique,

Maybe a case of the definition of "equation"? For me, that means higher mathematics (algebra, at least, and with photography, fiddling with square roots, etc.) and actually doing calculations in the field. Maybe the better question might be, "which equations do you calculate with in your head in the field?" My answer: none.

Sure, I know the inverse square law and the "Sunny-16" rule, and I even have a good idea of a logarithmic curve for reciprocity adjustments with a constant gradient, and I can multiply filter factors in my head if I have to. I even know the square root of 2 to a few decimal places :-)

But, knowing the equations and using them, i.e., plugging in values and calculating, in my head instead of with a calculator or paper at that, is something I never do in the field. I know where to look in my guide book, and that's faster for me.

I suppose I would be happy to use "Sunny 16" if my light meter stopped working, however, as long as it's functioning, I'm not going to guesstimate, rather be as precise as I can. Sometimes I'll use the same exposure for a similar lighting situation without re-metering if I know the light has not changed, but, if I have time, I'll meter anyway.

I meter through my filters for other reasons than avoiding calculating filter factors. With this technique, however, I only have to remember (not calculate) a few "fudge factors" when using strong filters. The same with exposure adjustments for contractions and expansions. "Add 2/3-stop" is not a calculation, just something I remember (and, if I forget, I've got it printed out in my handy guide book).

As for bellows extension, I carry a small tape measure and consult my tables. Again, no calculating... I might even omit the measuring step and estimate the distance, but I would check the table to find the exposure.

And, I've read Merklinger and understand Scheimpflug, but I never calculate a tilt or a swing, preferring instead to use the ground glass. And, I work for a rather small CoC and always try to use an optimum f-stop. But again, I've done the calculations at home so in the field finding the optimum f-stop is a matter of simply measuring focus spread and consulting the little chart taped to my camera body. And, I took physics of optics classes at university alongside my music classes; did lots of ray tracing, etc. I don't use those equations in the field either.

I think it really helps to understand the physics behind what we do as photographers. It helps us understand the medium and exploit all the possibilities (e.g., Damn it! I know I can get that in focus if I just find the right tilt/swing combination! Let's start over from zero position...)

So, If you asked "how aware are you of the science behind your photography when working?" I would answer, "very." That said, I'm not good at crunching numbers in my head, and don't do that in the field.

Best (and fun thread)

Doremus

[Ole Tjugen]

ALL of them, I think - I'm trained in science, and have no difficulties doing any necessary calculations in my head. I find it far easier to do mental maths than to remember where I put my written notes - or at least I think I once had some written notes?

Quite useful to me are the calculations to work out effective focal length from any combination of cells. Especially when I use a Speed Graphic and a pocket full of casket sets...

[Ari]

When in doubt, shoot a Fujiroid.

[Tintype Bob]

Sunny Sixteen

Sunny day - ASA = Shutterspeed @ f16

ie: asa 100 = 100/th second @f16

[DrTang]

I have enough trouble remembering that the bigger the number - the little'r the hole