All extension tubes are designed to enable a camera lens to focus closer than a lens minimum object distance (MOD) for more magnification. Pentax 67 extension tubes are mounted to the inner bayonet of Pentax 6X7/67/67II cameras and permit automatic diaphragm operation with interchangeable lenses of 45mm — 300mm focal length. This article covers only Pentax 67 extension tubes for the inner bayonet. Extension tubes for the outer bayonet lack automatic diaphragm operation but the mathematics are the same.
The exposure factor is a value by which shutter speed should be multiplied to get the film properly exposed when doing a macro or close-up shot with the lens extended by extension tubes.
The further the lens moves forward, the greater the distance between lens and film plane, and the less amount of light reaching the film. Therefore exposure must be increased to compensate for the loss of light. This is called the “exposure factor”.
To calculate exposure factor (EF) properly you need to know three parameters: focal length (f), lens helicoid extension (He) and total length of the extension tubes (Te). This is a formula to calculate exposure factor: EF = ( (f + Te + He ) / f )2.
We already know the focal length. Pentax 67 extension tubes were produced as a set of three tubes of different length: #1 — 14mm, #2 — 28mm, and #3 — 56mm. See the top image for details. Now, we can calculate the total length of the set of tubes that we are working with. So, all we have to do is to measure the lens helicoid extension.
by adding together all the required figures
Lens helicoid extension
Most lenses are made in such a way that no exposure compensation is required when you shoot at maximum helicoid extension because the loss of light in such case amounts not more than 0.3EV, which is easily superseded by the exposure latitude of the film. That is why people typically disregard calculating the exposure factor, except for some lenses with the minimum focal distance less than 8× of the lens focal length.
However, it should be figured out in macro photography with the use of extension tubes to accurately determine exposure, as the lens is already extended by tubes and additional helicoid extension leads to a sharp increase in exposure factor.
For instance, the maximum helicoid extension of a 90mm F2.8 lens is 22mm, and in the case of 135mm F4 Macro lens it amounts to 42mm, which is equivalent to tubes #1+2. Thus, exposition should be adjusted in such lenses under maximum extension even when they are used without any extension tubes: +0.5EV and +0.8EV respectively.
Well, it is not difficult to measure helicoid extension with a regular ruler. Please take a look at the image detailing how to do it. I’ve used 135mm F4 Macro for example. In the top image, the focus is set to the infinity — red mark at 10mm. In the bottom image, the focus is set to the closest distance — the red mark at 52mm. So, the helicoid extension is 42mm.
Pentax 67 extension tubes & Exposure compensation calculator
No we can proceed to calculate exposure factor. I’ve made a simple calculator which facilitates this function for Pentax 67 most popular lenses: 90mm F2.8, 105mm F2.4, 135mm F4 Macro, 150mm F2.8 and 165mm F2.8.
To carry out calculations you should first select a lens from the list and a combination of extension tubes which you use for your purposes, as well as lens helicoid extension, whose calculation I’ve already described. The exposure factor will be calculated automatically.
You can also specify the shutter speed which you’ve measured with an exposure meter. The appropriate shutter speed will be calculated with regard to an exposure factor.
As a bonus, the calculator provides additional useful data for macro work: magnification, effective lens speed, and picture area.
Life size ratio
There is a rule: to get 1:1 magnification with any lens you need to extend it by its focal length. For example, to get 1:1 with 105mm F2.4 you need to use tubes #1+2+3 (98mm) and helicoid extension by 7mm, for 90mm F2.8 you need tubes #2+3 (84mm) and helicoid extension by 6mm, and for 135mm F4 Macro you need to use tubes #1+2+3 (98mm) and helicoid extension by 37mm. In this case the exposure factor will be x4 that gives +2EV of exposure compensation.
Exposure compensation without extension tubes
Yes, you may need it. But it depends on the lens you use and the helicoid extension. It is better to check this with the calculator. In my experience, if the loss of light is more than 0.3EV you would better to adjust exposure.
Pentax 67 extension tubes magnification chart
|45mm F4||0.31 ~ 0.48||0.62 ~ 0.79||0.93 ~ 1.1||1.24 ~ 1.41||1.56 ~ 1.72||1.87 ~ 2.03||2.18 ~ 2.34|
|55mm F4 (I)||0.25 ~ 0.45||0.51 ~ 0.71||0.76 ~ 0.96||1.02 ~ 1.22||1.27 ~ 1.47||1.53 ~ 1.73||1.78 ~ 1.98|
|55mm F4 (II)||0.25 ~ 0.49||0.51 ~ 0.75||0.76 ~ 1.0||1.02 ~ 1.25||1.27 ~ 1.51||1.53 ~ 1.76||1.78 ~ 2.02|
|90mm F2.8||0.16 ~ 0.36||0.31 ~ 0.51||0.47 ~ 0.67||0.62 ~ 0.82||0.78 ~ 0.98||0.93 ~ 1.13||1.09 ~ 1.29|
|105mm F2.4||0.13 ~ 0.27||0.27 ~ 0.4||0.4 ~ 0.53||0.53 ~ 0.67||0.67 ~ 0.8||0.8 ~ 0.93||0.93 ~ 1.07|
|135mm F4 Macro||0.1 ~ 0.41||0.21 ~ 0.52||0.31 ~ 0.62||0.41 ~ 0.73||0.52 ~ 0.83||0.62 ~ 0.93||0.73 ~ 1.04|
|150mm F2.8||0.09 ~ 0.23||0.19 ~ 0.32||0.28 ~ 0.41||0.37 ~ 0.51||0.47 ~ 0.6||0.56 ~ 0.69||0.65 ~ 0.79|
|165mm F2.8||0.08 ~ 0.21||0.17 ~ 0.3||0.25 ~ 0.38||0.34 ~ 0.47||0.42 ~ 0.55||0.51 ~ 0.64||0.59 ~ 0.72|
Pentax 67 extension tubes offline calculator
Finally, I’ve decided to make a spreadsheet calculator for Microsoft Excel, LibreOffice Calc, or a similar program. Follow this link to download it. Thanks to the reader who requested this option.
Extension tubes mathematics
If you are interested in learning more about mathematics of extension tubes, read this article by Douglas A. Kerr The Mathematics of Extension Tubes in Photography.
Let me know If you would like me to add other lenses to the calculator. I will do it as soon as I possibly can.