View Full Version : Formula for adjusting Focal Length with Close-up Lenses

Anyone know of a formula -- or other way -- to calculate the "new" focal length when you add a close-up or supplementary filter/lens to a given lens?

I know that a CU lens has its own focal length and it will shorten the focal length of the lens to which it is attached, but I would like to have an easy way to know by how much. For example, a #1 (1,000mm) CU lens will decrease the focal length of a 100mm lens a little, but a #2 (500mm) CU lens will decrease it even more. In both cases, the lens requires refocusing for use at infinity and it should not affect the exposure much at all, but I would like to know what the focal length would be before I choose a CU lens. Of course, with higher diopter lenses you need to watch out for vignetting.

Something like: X = Y / (1 + (Z / 10)) would be easy enough.

where:

X = the new (or adjusted) focal length

Y = the old (or starting) focal length

Z = the diopter (not the focal length) of the close-up lens attached

Examples:

135mm = 150mm / (1 + (1 /10))

75mm = 90mm / (1 + (2 /10))

Mark Sawyer

15-Sep-2015, 11:01

With the camera focused, measure the distance from the lens' aperture to the ground glass. (A)

Measure the aperture with the close-up lens on, (through the close-up lens). (B)

Divide A by B. That's the f/stop. This also compensates for any bellows extension factor.

Thanks, but I'm not looking for the f-stop. Adding CU filters does not change the f-stop much. I'm looking for an easy way to calculate the NEW focal length BEFORE I attach the close-up lens.

With the camera focused, measure the distance from the lens' aperture to the ground glass. (A)

Measure the aperture with the close-up lens on, (through the close-up lens). (B)

Divide A by B. That's the f/stop. This also compensates for any bellows extension factor.

Maris Rusis

15-Sep-2015, 12:57

I'd use Gullstrand's Equation. You need to know the location of the Principle Planes of the lenses involved. The close-up lens is a "thin" lens and the principle plane is practically where the lens is. The main lens usually has its principle plane about where the iris diaphragm is. Basically you add the powers of the two lenses (in dioptres) and subtract the product of the powers and the distance between them (in centimetres). The answer is the new power in dioptres. It's a pleasant subject to study and the internet has plenty on it.

Mark Sawyer

15-Sep-2015, 13:23

Thanks, but I'm not looking for the f-stop. Adding CU filters does not change the f-stop much. I'm looking for an easy way to calculate the NEW focal length BEFORE I attach the close-up lens.

My apologies! The easiest way (I think) would be to convert everything to diopters. Diopters are just the inverse focal length of the lens in meters. So a 2 diopter lens is 1/2 a meter's focal length (500mm), a 3 diopter lens is 1/3 a meter's focal length (533mm), a 10 diopter is 1/10 of a meter in focal length (100mm), etc... You can add two different diopters to get a cumulative power, so a 2 diopter (500mm) plus a 3 diopter (333mm) would make an 5 diopter (200mmn) lens.

So if your lens is a 300mm, it's 3.3 diopter, (because 1000mm divided by 300mm is 3.3). If you add a 2 diopter (500mm) lens, you have a total of 5.3 diopters, (2 + 3.3). Divide 1000mm by 5.3, and you get 188.6mm, your combined focal length.

Make sense?

Mark Sawyer

15-Sep-2015, 13:29

And Maris is quite right about Gullstrand's Equation, but at the spacings we're using, just adding diopter powers will be very close.

That sounds great, but I am missing something.

Here is an updated formula:

X = 1000 / ((Y / 1000) + Z)) / 5.3

X = the new (or adjusted) focal length

Y = the old (or

starting) focal length

Z = the diopter (not the focal length) of the close-up lens attached

Here is what I get:

X = 1000 / ((Y / 1000) + 1)) / 5.3

Example:

5000 = 1000 / ((90 / 1000) + 1)) / 5.3

Something is wrong here.

My apologies! The easiest way (I think) would be to convert everything to diopters. Diopters are just the inverse focal length of the lens in meters. So a 2 diopter lens is 1/2 a meter's focal length (500mm), a 3 diopter lens is 1/3 a meter's focal length (533mm), a 10 diopter is 1/10 of a meter in focal length (100mm), etc... You can add two different diopters to get a cumulative power, so a 2 diopter (500mm) plus a 3 diopter (333mm) would make an 5 diopter (200mmn) lens.

So if your lens is a 300mm, it's 3.3 diopter, (because 1000mm divided by 300mm is 3.3). If you add a 2 diopter (500mm) lens, you have a total of 5.3 diopters, (2 + 3.3). Divide 1000mm by 5.3, and you get 188.6mm, your combined focal length.

Make sense?

To use the Gullstrand eq, you need to consider the distance between the two lenses or thickness of the added lens.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/gullcal.html

David

So are you saying there is no easy way to compute the NEW FL?

To use the Gullstrand eq, you need to consider the distance between the two lenses or thickness of the added lens.

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/gullcal.html

David

Mark Sawyer

16-Sep-2015, 11:33

Could you tell us the focal length of the lens you're going to use and the diopter you'll be adding?

You could also just put the diopter on and measure the focal length manually...

I don't want to measure the optical focal length of the lens (don't people know what that is) or know what diopter CU lens I will be using. I want an easy formula to compute the focal length of a given lens with a given diopter?

Seems simple enough to me. Remember -- SIMPLE.

Could you tell us the focal length of the lens you're going to use and the diopter you'll be adding?

You could also just put the diopter on and measure the focal length manually...

The whole pint is to have a formula that you can add in the FL and CU diopter and get a result.

OK, I'm looking for a UNIVERSAL formula where I know the FL of the lens but variable, and the diopter or FL of the CU lens -- variable. I do not want to measure anything physically.

What would the optical focal length of a 90mm lens be if I added a #2 CU lens? How can I tell in ten seconds?

Could you tell us the focal length of the lens you're going to use and the diopter you'll be adding?

You could also just put the diopter on and measure the focal length manually...

So are you saying there is no easy way to compute the NEW FL?

No, that is not what I wrote. I was simply pointing out you were missing a distance parameter in comparison of your eq vs the Gullstrand. Sorry, as I tried to help.

David

Mark Sawyer

16-Sep-2015, 17:07

OK, I'm looking for a UNIVERSAL formula where I know the FL of the lens but variable, and the diopter or FL of the CU lens -- variable. I do not want to measure anything physically.

What would the optical focal length of a 90mm lens be if I added a #2 CU lens? How can I tell in ten seconds?

I know you're looking for a universal formula, but when we give them to you, you don't quite seem to grasp them. Gullstrand's Equation is more complex and using a complex lens system on one side, needs some data most won't have, which is why I gave a simpler approach. Not as accurate as a full Gullstrand's Equation, but close enough for practical field work. I thought having an actual lens to apply it to and walk you through it again might help...

A 90mm lens has a diopter power of 11.111... (1000mm divided by 90mm)

A 2x diopter has a diopter power of 2 (!)

11.111 + 2 = 13.111. That's your total diopter power.

1000mm divided by 13.111 = 76.27mm. That's the combined focal length with the simplified method.

Comparing that to a simplified version of Gullstrand's Equation can be done using this online calculator:

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/gullcal.html#c1

Type 2 into the first box, 11.111 into the second box, and 1 cm separation (just a guess) into the third, and it gives a copmbined diopter power of 12.88878, and a focal length of 7.7586cm, or 77.586mm, or 1.316mm difference from my figure. As I said, close enough...

But the online calculator considers your 90mm lens as a single thin lens, so it will be off by a bit too, but again, it's still close enough for practical field work.

I hope this helps...

All I want is a simple formula to use in the field. I want to do it in my head. A+B=C. So far I have

NEW FL = OLD FL / (CU diopter / 10)

So 90 = 100 / 10.

I know you're looking for a universal formula, but when we give them to you, you don't quite seem to grasp them. Gullstrand's Equation is more complex and using a complex lens system o

n one side, needs some data most won't have, which is why I gave a simpler approach. Not as accurate as a full Gullstrand's Equation, but close enough for practical field work. I thought having an actual lens to apply it to and walk you through it again might help...

A 90mm lens has a diopter power of 11.111... (1000mm divided by 90mm)

A 2x diopter has a diopter power of 2 (!)

11.111 + 2 = 13.111. That's your total diopter power.

1000mm divided by 13.111 = 76.27mm. That's the combined focal length with the simplified method.

Comparing that to a simplified version of Gullstrand's Equation can be done using this online calculator:

http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/gullcal.html#c1

Type 2 into the first box, 11.111 into the second box, and 1 cm separation (just a guess) into the third, and it gives a copmbined diopter power of 12.88878, and a focal length of 7.7586cm, or 77.586mm, or 1.316mm difference from my figure. As I said, close enough...

But the online calculator considers your 90mm lens as a single thin lens, so it will be off by a bit too, but again, it's still close enough for practical field work.

I hope this helps...

This is not Rocket Surgery. All I have at this point is:

NEW FL = OLD FL / (DIOPTER + 10)

Here's what we got:

NEW fl = OLD fl / 1 + (diopter / 10)

Examples:

82mm = 90mm / 1 + (1.1)

75mm = 90mm / 1 + (2.1)

64mm = 75mm / 1 + (2.1)

OOPS:

I meant :

NEW fl = OLD fl / (diopter / 10)

Examples:

82mm = 90mm / 0.1

75mm = 90mm / 0.2)

64mm = 75mm / 0.1)

Here's what we got:

NEW fl = OLD fl / 1 + (diopter / 10)

Examples:

82mm = 90mm / 1 + (1.1)

75mm = 90mm / 1 + (2.1)

64mm = 75mm / 1 + (2.1)

Kirk Gittings

17-Sep-2015, 10:46

I'm curious as to why it matters-just curiosity? I have to say I never even thought about the effect of a CUL on focal length.

Mark Sawyer

17-Sep-2015, 11:17

I'm curious as to why it matters-just curiosity? I have to say I never even thought about the effect of a CUL on focal length.

Well, since it affects focal length, and it also affects aperture (as the CU lens magnifies the opening), it affects f/stop, so it's nice to know it for exposure calculation. And for some of us lens-nerd types, it's nice just to understand how things work.

Mark Sawyer

17-Sep-2015, 11:26

All I want is a simple formula to use in the field. I want to do it in my head. A+B=C. So far I have

NEW FL = OLD FL / (CU diopter / 10)

So 90 = 100 / 10.

I'll try one more time:

the formula is A+B=C

A = original lens diopter power

B = CU lens diopter power

C = combined diopter power

You can then convert diopter power to mm for focal length with the formula:

1000/C

Let's say your widest lens is 90mm. If you want a wider one, just add on a supplementary lens. A #1 supplementary lens converts your 90mm lens to a 82mm lens. A #2 supplementary lens converts your 90mm lens to a 75mm lens. It saves the cost a new lens. Get it?

I'm curious as to why it matters-just curiosity? I have to say I never even thought about the effect of a CUL on focal length.

Mark Sawyer

17-Sep-2015, 11:46

Let's say your widest lens is 90mm. If you want a wider one, just add on a supplementary lens. A #1 supplementary lens converts your 90mm lens to a 82mm lens. A #2 supplementary lens converts your 90mm lens to a 75mm lens. It saves the cost a new lens. Get it?

It also creates a lens with a different optical formula that's far less than optimum. Expect a few aberrations to show up, (field curvature, coma, astigmatism, chromatic aberration, maybe some barrel distortion). The formula is:

A+B=C

A = a good lens

B = cheap modifier

C = piece of shit lens

Mind you, some of us love our piece of shit lenses! But then, shit is an acquired taste, I suppose... :)

Kirk Gittings

17-Sep-2015, 12:41

Let's say your widest lens is 90mm. If you want a wider one, just add on a supplementary lens. A #1 supplementary lens converts your 90mm lens to a 82mm lens. A #2 supplementary lens converts your 90mm lens to a 75mm lens. It saves the cost a new lens. Get it?

I understand that with your example of a "supplementary lens" (good lens becomes crap lens) but you were talking about a close-up lens which I never thought of as changing the focal length.

OMG. I never thought that this would create a fire storm. All I wanted was a simple formula. And I got it. The question was NOT if it would degrade the quality of the result.

FYI There are many top-notch CU lenses such as Minolta and Nikon -- with two elements. Most CU lenses are single element, but you are only using the center portion of the image and you will not notice any degradation.

Mark Sawyer

17-Sep-2015, 14:03

FYI There are many top-notch CU lenses such as Minolta and Nikon -- with two elements. Most CU lenses are single element, but you are only using the center portion of the image and you will not notice any degradation.

The doublets will be achromatic, getting rid of the color fringing from chromatic aberration, but the other aberrations will remain. You'll also have a smaller image circle with any close-up lens, but even a bit more so with the thicker doublets.

Back to the original thread. Any one have a formula?

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