Shooting Macros Section 3 – The Math

by Peter Zack

  

Note: I hope some of the first two Macro sections has helped you understand equipment and shooting. As is the funny thing with a blog publishing setup, the articles are posted by date and you may be seeing the last part first. If so, go to Part 1 and Part 2 and then come back to this next section in the series, in which we will look at the math and magnification factors in a bit more detail. Also if you have a question or ideas for this or other articles, contact us here.

This stuff can sound a bit boring but for those that want to know how close they can get with a certain setup, we’ll have a look at the math here.

You can test it yourself: First you can approximate the magnification of any macro set-up with a little careful test and a ruler on the kitchen table. All you need to know is the width of the sensor of your camera. So a Pentax K20D has a sensor size of 23.4W x 15.6L (mm). Use a ruler with clear measurements in millimetres. Focus the camera/lens combination at full extension, sharply on the ruler with the sensor plane as parallel as you can (straight down). Take a picture of the ruler and open the shot on your computer. It’s a simple matter of counting the number of millimetres across the image. If you got 18mm then the magnification would be 1.3x (23.4 / 18). With a Canon EOS 40D, the sensor width is 22.2mm. Using the same result the magnification would be 1.23x (22.2 / 18). This is about the only way you could calculate the magnification of a reversed lens, a pair of lenses stacked and possibly some filter add on macro lenses to a standard lens.

Stacked lenses referred to here for example could be a 50mm lens mounted normally to the camera and then using a filter ring which couples another lens reversed on the first lens. Similar to reversing a lens directly to the camera but with even greater magnification.

Reversed lens with extension tubes: To calculate the magnification with a reversed lens and extension tubes, you first have to do the test above and get as accurate a measurement as possible of the reversed lens’s magnification.

The Pentax FA50mm f1.4 when reversed on a K20D (sensor size 23.4mm) is 35mm (using test above)
MR: (23.4 / 35) = 0.67x

Formula: Mm = MR + (Ex/FL)
Mm: magnification in macro
MR: magnification of the Lens reversed
FL: focal length of lens
Ex: length of extension tubes

If we used a 31mm Pentax K mount extension tube, mounted to the camera, mount the lens to that tube with a 49mm (filter) to K mount adapter, we have about 34mm of extension (tube + adapter). The Macro Magnification is 1.35x = 0.67 +(34/50)

Extension tubes or Bellows: To calculate the effect of a set of tubes you will first need the magnification specifications of the normal lens you will add to the tubes. (Not a macro lens)

Formula: Mm = ((ML x FL)+Ex) / FL
Mm: magnification in macro
ML: magnification of the Lens
FL: focal length of lens
Ex: length of extension tubes

So for the first example we’ll use the Canon EF 50mm f/1.4 USM which has a maximum magnification of 0.15x alone. We will add 62mm of extension tubes to this lens.

1.39 = ((0.15 x 50) + 62) /50 in other words the lens can achieve 1.39x life sized. So you will get a little better than life sized with this setup.

Stacking lenses: All you need here is a filter adapter to reverse one lens and mount it to the filter end of a primary lens.

Formula: Mm = F1 / FR
Mm: magnification in macro
F1: Focal length of first lens
FR: Focal length of reversed lens

Example calculation could be a 200mm lens mounted to the camera body in the normal fashion and a 50mm lens reversed to the 200mm lens.

4 = 200/50

It would appear that I have ignored probably the most obvious; a macro lens and extension tube/bellows combination. I can’t determine or find a satisfactory formula that gives accurate results. The reason is that a dedicated macro lens might be 100mm in normal mode but when extended, the focal range changes because the lens has essentially a helical extension tube built in. So the macro focal length might be 72mm for that particular lens. But lens suppliers do not publish that focal length change. Without that data, formulas are inaccurate. You should be able to use the formula for Extension tubes and Bellows above but the calculation could be off by as much as 30%.

Tele-converters: A TC and a conventional lens. If the lens has a magnification of 0.25 at minimum focus then the TC will multiply that close up ability by the magnification it was designed for (1.4x, 2x, 3x, etc.). I.e.: 0.25 x 2 = 0.5 magnification or 1:2 (half life sized).

P&S and Pro-sumer cameras: Finally a note on Point & Shoot cameras that can offer a different option and advantage to some people who like close-up shooting. The P&S disadvantage is that most do not shoot in RAW and the sensors can be small, so there may be more noise in the shots and less ability to crop a shot afterwards. But many bridge cameras overcome these limits very well. Both these styles of cameras use very small sensors (commonly 1/1.8″ or 1/1.25″) and so when the camera is listed as an equivalent lens of  450mm (in 35mm terms) it is really about a 77mm or 95mm focal length lens. The longer lens equivalent will give greater working distances and the smaller sensor increases the apparent DOF. A good and inexpensive option for many shooters.

So what can you get after some practice and reading the 3 sections of this article? Grzegorz Cywicki of Zabierzów, Poland has some amazing macros to share, just click on the photo above to see a sample of his work—all the photos illustrating part 3 of this series, were taken by him. He uses a fairly basic setup. A sub $500 camera with a few different setups. A dedicated macro lens (Tamron 90mm f2.8) and extension tubes from 60 to 130mm. A 21mm extension tube and a Tamron 75-300mm zoom. Also a Tamron 75-300mm with Raynox DCR-250 which we discussed in the first section of this series.  He uses natural light whenever possible and also diffused flash, off camera with some shots and reflectors with others.

All the subjects are alive and you will notice water drops on some shots. He carries a spray bottle of cold water with him to slow the insects down. Other times he will shoot early in the morning when it’s cool and they move slower.

When asked about the incredible Dragonfly shots, Grzegorz simply said: “A key to success is to know how the dragonfly behaves. They fly around their own territory and almost always they come back to the same place. Usually, before I decide to take [the] pictures, I’m trying to observe them. As I know where dragonflies most often come back, I take [the] pictures.”

If you would like to contact  Grzegorz by email, please go to the contact page and we’ll forward his email address to you.

If you have any additional information you would like to add to this topic or have a question, Please leave a comment below or send us an email from the contact page.

Cheers and good shooting –Peter Zack

All photos section 1&2: ©Peter Zack.

All photos section 3: ©Grzegorz Cywicki.