PDA

View Full Version : FORMulae

johnielvis
24-Sep-2011, 17:46
sick of seeing people being confused.

since I've been a working with the 1100 xxl a LOT lately on the studio cam in the apartment, i've needed to do some lens calculations....a LOT of lens calculations...tiring of that, I derived some formulas....HERE's what I've derived that are VERY useful for limited space...

first off--everyone knows--exposure "bellows" factor = (1 + M)^2

where M is magnification.

Second--bellows DRAW--total s' distance from lens aperture to ground glass is:

s' = (1 + M)*f

where M is magnification and f is focal length

so the 180mm lens at 2:1...bellows would be 180*(1+2) = 540mm

THIRD...important for close quarters is

TOTAL distance from subject to ground glass= d

d = f*(2 + M + 1/M)

that means at .5 magnification total distance from subject to gg = (2 + .5 + 1/.5)*f = 4.5*f

so the 180mm lens at 2:1 would be 4.5*180 = 810mm total distance.

now for the fun stuff...say you have a lens of focal length f and want to know the magnification possible for a distance d (the above total distance you have from camera back to subject front)...this is:

M = (d/2f - 1) - sqrt( (d/2f - 1)^2 - 1 )

this comes in handy when determining what lens you can use in what room depending on how big a field you want....

I LoVE this stuff....

Leigh
24-Sep-2011, 22:42
Nice equations. Too bad they're not accurate.

They're derived from thin lens equations. The significant error is that thin lens equations are based on the first and second principle planes being coincident. That's seldom true with a compound lens.

The distance from the lens aperture (usually the lensboard) to the ground glass when focused at infinity (your s') is the Flange Focal Length (FFL) of the lens, which may be substantially different than its optical focal length, particularly with long lenses. The FFL is given on lens data sheets.
As an example, the FFL for the 1200mm Nikkor-T lens is only 756mm.

If you want to achieve 1:1 magnification you must extend the lens from its infinity focus position by a distance equal to its optical focal length, so the equation for the extension (change in distance) is d = m * f. The total distance from lensboard to gg would be FFL + d.

- Leigh

cosmicexplosion
25-Sep-2011, 04:02
Nice equations. Too bad they're not accurate.

ahhh made me laugh. my only laarrff today. well done.

johnielvis
25-Sep-2011, 15:09
made me laugh too...see what I'm saying about people getting it wrong.

the equations are EXACT...and they work perfectly and were tested with the olde measuring tape and work out perfectly for me and my 1200xxl...of course it's a symmetical lens.

however, for the bizarre telephoto condition that leigh brings up...he's right....but all you gotta do is substitute the position of the rear nodal point for the aperture position for such a case----I tested this with the three teles I got and it also works perfectly and exactly.

you can measure the rear nodal point by focusing on something at infinity and then stretching out your measurement tape to the focal length of the lens...for a tele, you'll see that this will generally be a point IN FRONT OF the lens....no biggie...just remember where that's located (3" in front, 4" in front, whatever)...and base your calcualations from that point using the above EXACT equations.

at any rate---when you're doing repro work--most of the lenses are totally symmetrical, so the equations work out exact anyways...that is...you're not using tele lenses in the regime I'm talking about 1:1---1:5 say....what kind of idiot buys a tele lens and then uses it for LONG bellows work like that ---- NOBODY, that's who.

tele lenses are meant for FAR, infinity focus with bellows-challenged cameras--show me a tele-repro lens...just one....they don't exist...WHY? tell us the answer~

yes...tell us tell us

25-Sep-2011, 15:55
Even symmetrical lenses have a non-zero nodal point separation.

Leigh
25-Sep-2011, 16:27
Well, johnielvis,

However, you're making some gross assumptions that cannot be substantiated. For example:
Long lenses are often used for closeup work, in situations where you need room for lighting or other support equipment, or where the subject cannot be approached.

Secondly, the FFL and the optical focal length are very seldom the same, across the entire range of focal lengths used for LF photography. This can be confirmed by reviewing the manufacturers' data sheets.

- Leigh

johnielvis
25-Sep-2011, 18:27
well they all seem to work perfectly for me to tape measure precision which is all I've ever needed...whatever error there is I haven't been able to measure. I don't have a micrometer adjustment on my studio camera..infact, I focus by moving the camera back and forth---it's in my apartment.

just curious, which formulas do YOU use when setting up a shot or choosing a lens? Or, if you don't need such formulae due to vast experience and judgement, which SHOULD I and others be using?....you state mine are totally erroneous...ok...if they are, then which ones SHOULD be used? please give them below and end this. Thank you.

Leigh
25-Sep-2011, 18:44
I didn't say the equations were erroneous. I said they were not accurate.

Accuracy is based on published measurements. Yours deviate from those by using optical focal length in a situation that requires flange focal length.

I was just pointing out the difference between the two parameters. In some cases it does matter.

Your equations are 'close enough' for most applications.

- Leigh

Ari
25-Sep-2011, 18:51
I didn't say the equations were erroneous. I said they were not accurate.

Accuracy is based on published measurements. Yours deviate from those by using optical focal length in a situation that requires flange focal length.

I was just pointing out the difference between the two parameters. In some cases it does matter.

Your equations are 'close enough' for most applications.

- Leigh

Or to paraphrase Leigh, if I may:

"I understand what you're saying, but you're completely wrong!" :)

Jay DeFehr
25-Sep-2011, 19:18
Maybe if the thread hadn't begun with...."sick of seeing people being confused.", and instead, something like, "Some useful formulas for close-up work". Just a thought.