Extension Tubes: Transforming Any Lens Into a Macro Powerhouse
A deep dive into the physics and mathematics of extension tubes, exploring how simple spacers can unlock macro photography capabilities in any lens
2015-07-10
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A deep dive into the physics and mathematics of extension tubes, exploring how simple spacers can unlock macro photography capabilities in any lens
I got into macro because cheap gear let me stare at ordinary things until they looked alien. Dedicated macro lenses were out of my budget. A $80 set of extension tubes was not.
Extension tubes are hollow spacers between your camera body and lens. No glass. You are just pushing the lens farther from the sensor.
That changes everything about focus distance and magnification. It sounds trivial until you try to focus on a bee at 1:1 and realize your lens has never behaved like this before.
Extension tubes work because of the thin lens equation:
1/f = 1/u + 1/v
Where:
f = focal length of the lensu = object distance (distance from lens to subject)v = image distance (distance from lens to sensor/film)Add a tube of length E and you increase image distance:
v_new = v + E
The magnification ratio M is defined as:
M = v/u
With extension tubes, this becomes:
M = (v + E)/u
For a lens focused at infinity without extension tubes, v = f (the focal length). So with extension tubes:
M = (f + E)/u
At minimum focusing distance, for many lenses:
M_max = E/f
Longer tube, more magnification. Shorter focal length, more magnification per millimeter of tube. That ratio is the whole game.
M_max = E/f = 25mm/50mm = 0.5x magnification
M_max = E/f = 25mm/100mm = 0.25x magnification
M_max = E/f = 25mm/25mm = 1.0x magnification (life-size)
Same 25mm tube. Very different result depending on the lens you bolt it onto.
Extension tubes are not free magnification.
Less light hits the sensor:
Light Loss Factor = (M + 1)²
For 1:1 magnification (M = 1):
Light Loss = (1 + 1)² = 4
That is 2 stops (since 2² = 4). Plan on a tripod or a flash earlier than you would without tubes.
The new minimum focus distance becomes:
u_min = f × (M + 1)
At high magnifications, depth of field gets brutal. The macro DOF formula:
DOF = 2Ncδ(M + 1)/M²
Where:
N = f-numberc = circle of confusionδ = subject distanceM = magnificationMagnification goes up, depth of field drops fast (quadratically in M).
What I actually shot with in 2015:
I lived in Live View. Autofocus at 1:1 on a cheap fifty is mostly theater.
If you own a set, you can stack them:
Total Extension = E₁ + E₂ + E₃ + ...
12mm + 20mm + 36mm is 68mm total. On a 50mm lens:
M_max = 68mm/50mm = 1.36x magnification
I stacked when I wanted more reach and accepted that focusing distance and light loss got worse.
At f/8 or f/11 you may still only have a few millimeters of sharp depth. I stacked when a single frame could not hold the subject:
Extension Tube Set: ~$50-150 Dedicated Macro Lens: ~$400-1200
No extra glass means your lens is still your lens. You lose light and working distance. You gain a way to find out if macro is something you will actually shoot before you buy a 100mm macro that sits in the bag.
Modern tubes kept electronic contacts on my Canon setup. Autofocus still struggled up close. IS helped less than I hoped. Lightroom lens profiles still behaved normally.
My Flickr album has the rest from this series. Feathers, fabric weave, water on leaves. The math is optional. Stack a tube, miss focus a dozen times, nail it once, and you will remember why you bothered.