Formula for adjusting Focal Length with Close-up Lenses

[xkaes]

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]

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.

[xkaes]

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]

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]

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]

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

[xkaes]

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?

[TXFZ1]

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...t/gullcal.html

David

[xkaes]

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...t/gullcal.html

David

[Mark Sawyer]

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...