Proper exposure compensation for extension tubes

[timllowe]

I've seen several formula for calculating the exposure compensation required when using an extension tube. The one I use (and that makes sense to me) is

compensation = (focal length of lens + length of ext. tube)² / (focal length of lens)²

But I've seen a few other very plausible calculations yielding different results. As I only own a 21mm extension, the differences between the different methods doesn't make much of a difference. (I only shoot at the nearest half stop!) But I'd like to know out of curiosity and in case I get a longer tube or a wider lens. (I have only used the tube with an 80mm Planar and a 50mm Distagon.)

If anyone can site an authoritative source, I'd be forever grateful. Well... momentarily grateful anyway...

 

[pentaxpete]

Factor by which you multiply exposure can be found : (M+1) 2 where 'M' is the Magnification if known or can be calculated -- how do you get that 'small ' 2 for 'squared' on your computer !

 

[timllowe]

At least on a PC, there is an application called "Charmap" that you can use to put special characters (like "²") on the clipboard.

Can you expand your answer? What are the units of measure? An example like an 80mm lens with 20mm extension? Can you sit a source?

Thanks in advance!

 

[pentaxpete]

Not good at Maths but here goes : say your object is 2 inches long and you take it close-up so that it measures 2 inches on the focus screen then the 'Magnification' is 'same-size' or '1' so ( 1+1 ) 2 == 4 so you give 4 times the exposure say two shutter speeds LOWER or open up aperture by two stops.

Using YOUR measures I would use the OTHER Formula -- difficult to TYPE on this Computer but it is : Focal Length Squared divided by Extension Squared : so 80x80 divided by 20x20 = 16 which is the factor by which you multiply the exposure in your sample.