Formula/computation for enlarger magnification?

M Carter · Dec 19, 2021

I'm currently doing wall projection, up to 30" or so. I'm planning on tearing up the darkroom to reach around 6' enlargements. 4x5 negs with 135 and 150mm glass (the 150 is a Rodagon "G", we'll see if I need it at these sizes).

Anyway, to aid in planning - is there a way to compute magnification - let's say I can easily have a 12' room span, with a movable/alignable vertical "easel"; is there a way to determine how large a print can be made with a 135 and a 150?

Or another option: Stick a neg with a 1" square in the carrier, and measure the size of the square's projection at 2', 3', 5' - if I graph that out, can I "extend" the enlarging power beyond what I'm able to physically measure right now, if that makes sense? Draw a "map" of sizes at each distance, extend the lines of the "cone" the sizes make as they increase, and have an accurate idea of how much size increase I get at further distances?

I need to determine if more walls needs to go!

I SUCK at math, but can grasp things conceptually (and I have a calculator!), open to ideas - thanks!

(And yes, I've sussed out alignment, moveable easel-surface, material fixing to said surface, processing and so on...)

Sirius Glass · Dec 19, 2021

As the distance from the lens increases the exposure increases as the square of the distance.

I would start with the 135mm and 150mm lenses, however remember the shorter the lens focal length for the same enlarger height [distance] the larger the image. Hence you will reach the larger prints faster with a shorter focal length lens sooner, again assuming that the shorter focal length lens will cover the 4"x5" negative.

Nodda Duma · Dec 20, 2021

Here’s first order approximations. Should get you close enough to set up and adjust.

Width of your desired print h(i), distance to wall d(i), width of negative, h(o) and distance to negative d(o) gives you magnification:

M = -[d(i)/d(o)] = h(i)/h(o)

and then also focal length.

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

Btw, the negative sign just means the image is inverted (naturally)

so like for h(i) = -72” wide print (sign convention, print is inverted) from h(o) = 5” wide negative, you have a magnification of -14.4. The distance to the wall for a 6’ print and a 150mm lens is about 7’ 6 3/4”. That’s getting kinda short for light fall-off at the corners (cos^4 law), but might be ok. If not you’d want a longer lens to project further and reduce light falloff due to that effect. It’s a trade-off between light fall off (with shorter lenses) and available distance to wall and/or enlarger focus adjustment (too long a lens and you run out of focus travel)

To reach a 12’ wall, you’d need a lens with a focal length of about 240mm (I’ll let you work through the math).

I worked through the equations in my head and did the math with a calculator. At work I would set the math up in Excel spreadsheet which lets you adjust variables without having to recalculate each time.

M Carter · Dec 21, 2021

Sirius Glass said:
As the distance from the lens increases the exposure increases as the square of the distance.

I would start with the 135mm and 150mm lenses, however remember the shorter the lens focal length for the same enlarger height [distance] the larger the image. Hence you will reach the larger prints faster with a shorter focal length lens sooner, again assuming that the shorter focal length lens will cover the 4"x5" negative.

Thanks, but I know all of that and have the formula for recalculating exposure based on distance. I'm trying to visualize print size as distance increases. My 150mm lens (G for Grande) is optimized for 20-40x enlarging, the 135 more like 10-20x.

M Carter · Dec 21, 2021

Nodda Duma said:
Here’s first order approximations. Should get you close enough to set up and adjust.

Thanks, just what I was looking for! I really just want an idea of "if I have enough room". And light falloff with the 135 is already rearing its head at 36" from the lens at F11.
My 150mm is optimized for something like 10-20x, the 150 G for 20-40x IIRC, so will need to consider that as well. There's a wall that can go if needed...

All of this work is shooting bromoil/lith/alt process prints to re-print on emulsion-coated canvas, so I can also do the copy negs a bit smaller, not use the entire 4x5 frame, or do a few size iterations and test.

Doremus Scudder · Dec 22, 2021

...and don't just compute for full-frame images. Leave room for cropping too, which means you'll need a bit more. For extreme crops, you can use the next shorter enlarging lens, say if you want to crop a 6x9-cm portion of a 4x5-inch negative, but for anything between that and full-frame you'll need to compensate with more distance from lens to paper.

Best,

Doremus

DREW WILEY · Dec 22, 2021

That nominally is about 14X if you're going as big as 6ft from 4X5 film. Unless you already own a 150 Rodagon G, there are other alternatives. If you have a big enough room to back off a little more, a 180 or 240 f/9 Apo Nikkor would be even better optically, give a more even field of illumination, and is corrected all the macro to infinity, unlike G's, which are recommended only for really big enlargement factors. Apo Nikkors are in their own by f/11, so won't be any slower to actually print with, but just a little dimmer for prior setup viewing. You'll also likely save quite a bit of money buying an Apo Nikkor because these were marketed as graphics process lenses, and are fairly common on the used market (except the 180), but were in fact quite expensive when new. (But don't opt for a 210/9 Process Nikkor because that's a lesser performance lens of different element configuration).

But if you need a 150, the Apo Rodagon N 150/f4 is rated for up to 15X magnification, and will therefore be both brighter, more versatile, and less rare than a Rodagon G 150 (which is optimized at 20X). The Apo Rodagon N's also have superb contrast and microtonal separation. I use one for even 6x9 enlargements.

M Carter · Dec 29, 2021

DREW WILEY said:
That nominally is about 14X if you're going as big as 6ft from 4X5 film. Unless you already own a 150 Rodagon G, there are other alternatives. If you have a big enough room to back off a little more, a 180 or 240 f/9 Apo Nikkor would be even better optically, give a more even field of illumination, and is corrected all the macro to infinity, unlike G's, which are recommended only for really big enlargement factors. Apo Nikkors are in their own by f/11, so won't be any slower to actually print with, but just a little dimmer for prior setup viewing. You'll also likely save quite a bit of money buying an Apo Nikkor because these were marketed as graphics process lenses, and are fairly common on the used market (except the 180), but were in fact quite expensive when new. (But don't opt for a 210/9 Process Nikkor because that's a lesser performance lens of different element configuration).

But if you need a 150, the Apo Rodagon N 150/f4 is rated for up to 15X magnification, and will therefore be both brighter, more versatile, and less rare than a Rodagon G 150 (which is optimized at 20X). The Apo Rodagon N's also have superb contrast and microtonal separation. I use one for even 6x9 enlargements.

I actually have a 150 Rodagon G, got a good deal on it a while back, haven't been able to test it yet. If nothing else it could help me dial in sizes. Saving all this to my notes though, thanks!

M Carter · Dec 29, 2021

Doremus Scudder said:
...and don't just compute for full-frame images. Leave room for cropping too, which means you'll need a bit more. For extreme crops, you can use the next shorter enlarging lens, say if you want to crop a 6x9-cm portion of a 4x5-inch negative, but for anything between that and full-frame you'll need to compensate with more distance from lens to paper.

Good advice, but all of this work (for now anyway) starts with 16x20 or 20x24 Bromoil or lith prints, from several composited negs. I photograph the final retouched prints 4x5 (delta 100/DD-X, may try that swanky Adox film); the copy work is dialed in to a 3.5-ish contrast grade and pretty much fills the 4x5 frame, usually there's a thin print of a step wedge in there to judge development moves. The "final" large prints are on canvas, coated with liquid emulsion (via HVLP sprayer) and then tinted with oil glazes. Cool look at 30" or so, but I want to go bigger.

Example, model shot on white seamless, the "wall" was a mockup about 2' tall and composited in the enlarger, no photoshop/etc:

DREW WILEY · Dec 29, 2021

Looks like you have some fun projects going!

M Carter · Dec 30, 2021

DREW WILEY said:
Looks like you have some fun projects going!

I lie awake figuring this stuff out in my head!
Wish I had a photo of my wife's face when she walked upstairs to see me building this set... plaster and pool noodles! She just kinda rolls her eyes and thinks, "Well, who wants a normal husband anyway??"

Sirius Glass · Dec 30, 2021

M Carter said:
I lie awake figuring this stuff out in my head!
Wish I had a photo of my wife's face when she walked upstairs to see me building this set... plaster and pool noodles! She just kinda rolls her eyes and thinks, "Well, who wants a normal husband anyway??"

Will she get your certified?

DREW WILEY · Dec 30, 2021

Yeah, reminds me of one of those alien movies where the octopus-like creature bursts out of even the dead corpse it once inhabited, which is now under that crypt-like thing in your photo. It also reminds me of what happens if I don't constantly pull out the long ropey strands of St Augustine grass which keep invading my lawn. If ignored, they're eventually grow out onto the sidewalk, and, anaconda-like, twist around puppies and little boys passing by, and slowly devour them.

M Carter · Dec 30, 2021

DREW WILEY said:
Yeah, reminds me of one of those alien movies where the octopus-like creature bursts out of even the dead corpse it once inhabited, which is now under that crypt-like thing in your photo. It also reminds me of what happens if I don't constantly pull out the long ropey strands of St Augustine grass which keep invading my lawn. If ignored, they're eventually grow out onto the sidewalk, and, anaconda-like, twist around puppies and little boys passing by, and slowly devour them.

I grew up in Michigan - when I moved to Texas and was working on the lawn, I was like "what are these VINES in my lawn??" and started tugging them up. Realized they ARE the lawn. I kinda miss the soft grass and individual blades, that St. Augustine must have been one tough SOB!

Formula/computation for enlarger magnification?

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