## Macro – How can I calculate how an extension tube works?

I think there are some formulas that you can use. In Matt Grum's view, I haven't tested these with zoom lenses, and to my current knowledge, they only apply to premium lenses (fixed focal lengths). You didn't specify any special zoom lenses, so …

The easiest way to calculate the magnification of a lens is the following formula:

``````  Magnification = TotalExtension / FocalLength
M = TE / F
``````

In order to calculate the magnification with an extension tube, you need to know the total extension, ie the extension provided by the lens itself and the extension provided by the extension tube. Most lens statistics today include intrinsic magnification. When we use the Canon 50mm f / 1.8 lens, the intrinsic magnification is 0.15 times. We can solve the built-in lenses as follows:

``````   0.15 = TE / 50
TE = 50 * 0.15
TE = 7.5mm
``````

The enlargement with additional extension can now be calculated as follows:

``````  Magnification = (IntrinsicExtension + TubeExtension) / FocalLength
M = IE + TE / F
``````

If we assume an additional extension of 25 mm via an extension tube:

``````  M = 7.5mm + 25mm / 50mm
M = 32.5mm / 50mm
M = 0.65x
``````

A fairly simple formula that we can use to calculate the magnification fairly easily, provided you know the intrinsic magnification of the lens (or its intrinsic extent). If we assume that the wonderful 50mm lens is the one you are expanding, create a 1: 1 macro. If you zoom in, you need an extension worth 50mm. The problem here is that if you add too much expansion, the level of the world that is in focus (the virtual image) could just end Within the lens itself. In addition, this requires a "simple" lens, one with very well-defined and known properties (i.e., a simple single element lens).

In a real-world scenario, certain lens properties are unlikely to be clearly understood. For internally focusing lenses or zoom lenses, the simple formula above is not sufficient to calculate exactly how high your minimum focusing distance and magnification can be for a certain lens, a certain focal length and a certain extent. There are too many variables, most of which are probably unknown to calculate a meaningful value.

Here are some resources I've found that contain some useful information that could help you in your efforts:

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## Plotting – Why does Tube treat this list of triple machine numbers differently than Line?

I have a number of dates that `Line` but enjoy quite well `Tube` seems to be causing a tantrum if I deliver the same record. The data:

``````data = {{-1214.2199935658107`,-848.2705321806565`,-0.00001416666666666664`},{-1244.2463057872262`,-804.5024679750907`,-0.000013333333333333296`},{-1272.6743663132045`,-759.6590618571543`,-0.000012499999999999979`},{-1299.4664556851817`,-713.7981785755134`,-0.000011666666666666634`},{-1324.5865758011587`,-666.978491137754`,-0.000010833333333333317`},{-1348.0004016604767`,-619.2595928877795`,-9.999999999999972`*^-6},{-1369.6752736128424`,-570.7021396907099`,-9.166666666666655`*^-6},{-1389.5802339318311`,-521.3680065458933`,-8.33333333333331`*^-6},{-1407.6861084082525`,-471.32044184944846`,-7.4999999999999655`*^-6},{-1423.9656304860086`,-420.62420257475856`,-6.666666666666648`*^-6},{-1438.3936024494813`,-369.34565482908965`,-5.8333333333333306`*^-6},{-1450.9470855141483`,-317.5528264957635`,-4.999999999999959`*^-6},{-1461.6056085442237`,-265.31540183164884`,-4.1666666666666415`*^-6},{-1470.3513836617653`,-212.70465174468688`,-3.333333333333324`*^-6},{-1477.169516316059`,-159.79329776504858`,-2.4999999999999523`*^-6},{-1482.0481974956165`,-106.65531215558806`,-1.666666666666635`*^-6},{-1484.9788666805996`,-53.3656608828774`,-8.333333333333174`*^-7},{-1485.9563357913094`,-1.0921533706287417`*^-11,0.`},{-1484.9788666806012`,53.36566088285824`,8.333333333333717`*^-7},{-1482.0481974956178`,106.6553121555689`,1.6666666666666891`*^-6},{-1477.1695163160618`,159.79329776502965`,2.5000000000000066`*^-6},{-1470.351383661767`,212.70465174466793`,3.3333333333333782`*^-6},{-1461.6056085442272`,265.3154018316305`,4.166666666666696`*^-6},{-1450.9470855141521`,317.55282649574525`,5.000000000000013`*^-6},{-1438.3936024494853`,369.3456548290715`,5.833333333333385`*^-6},{-1423.9656304860139`,420.62420257474065`,6.666666666666702`*^-6},{-1407.6861084082593`,471.320441849431`,7.50000000000002`*^-6},{-1389.5802339318382`,521.3680065458755`,8.333333333333337`*^-6},{-1369.67527361285`,570.7021396906931`,9.166666666666709`*^-6},{-1348.0004016604855`,619.2595928877626`,0.000010000000000000026`},{-1324.58657580117`,666.9784911377373`,0.000010833333333333344`},{-1299.4664556851928`,713.7981785754989`,0.000011666666666666715`}};
``````

Entered in:

``````Grid[{{Graphics3D[{
{Darker[Green, 2/3], Thickness[0.01],

}, AlignmentPoint -> Center, AspectRatio -> Automatic,
AutomaticImageSize -> False, Axes -> False, AxesEdge -> None,
AxesLabel -> None, AxesOrigin -> {1650.`, -1650.`, -0.00025`},
AxesStyle -> {}, Background -> None,
BaselinePosition -> Automatic, BaseStyle -> {}, Boxed -> False,
BoxRatios -> {3.2`, 3.2`, 6.5`}, BoxStyle -> {},
ClipPlanes -> None, ClipPlanesStyle -> Automatic,
ColorOutput -> Automatic, ContentSelectable -> Automatic,
ControllerLinking -> Automatic, ControllerMethod -> Automatic,
ControllerPath -> Automatic, CoordinatesToolOptions -> Automatic,
DisplayFunction -> Identity, Epilog -> {}, FaceGrids -> None,
FaceGridsStyle -> {}, FormatType -> TraditionalForm,
ImageMargins -> 0.`, ImagePadding -> All, ImageSize -> 500.`,
ImageSizeRaw -> Automatic, LabelStyle -> {},
Lighting -> Automatic, Method -> Automatic, PlotLabel -> None,
PlotRange -> {{-2475.`,
1815.0000000000002`}, {-1815.0000000000002`,
2475.`}, {-0.00032500000000000004`, 0.00032500000000000004`}},
PlotRangePadding -> Automatic, PlotRegion -> Automatic,
PreserveImageOptions -> Automatic, Prolog -> {},
RotationAction -> "Fit", SphericalRegion -> True, Ticks -> None,
TicksStyle -> {}, TouchscreenAutoZoom -> False,
ViewAngle -> 0.33632810973764027`,
ViewCenter -> {0.5`, 0.5`, 0.5`}, ViewMatrix -> Automatic,
ViewPoint -> {-1.9461497767487252`, 1.477527579217831`,
2.340814665690469`}, ViewProjection -> Automatic,
ViewRange -> All, ViewVector -> Automatic,
ViewVertical -> {0.23556268765910476`, -0.24706981260320413`,
0.9399291079028442`}], Graphics3D[{
{Darker[Green, 2/3], Thickness[0.01],

}, AlignmentPoint -> Center, AspectRatio -> Automatic,
AutomaticImageSize -> False, Axes -> False, AxesEdge -> None,
AxesLabel -> None, AxesOrigin -> {1650.`, -1650.`, -0.00025`},
AxesStyle -> {}, Background -> None,
BaselinePosition -> Automatic, BaseStyle -> {}, Boxed -> False,
BoxRatios -> {3.2`, 3.2`, 6.5`}, BoxStyle -> {},
ClipPlanes -> None, ClipPlanesStyle -> Automatic,
ColorOutput -> Automatic, ContentSelectable -> Automatic,
ControllerLinking -> Automatic, ControllerMethod -> Automatic,
ControllerPath -> Automatic, CoordinatesToolOptions -> Automatic,
DisplayFunction -> Identity, Epilog -> {}, FaceGrids -> None,
FaceGridsStyle -> {}, FormatType -> TraditionalForm,
ImageMargins -> 0.`, ImagePadding -> All, ImageSize -> 500.`,
ImageSizeRaw -> Automatic, LabelStyle -> {},
Lighting -> Automatic, Method -> Automatic, PlotLabel -> None,
PlotRange -> {{-2475.`,
1815.0000000000002`}, {-1815.0000000000002`,
2475.`}, {-0.00032500000000000004`, 0.00032500000000000004`}},
PlotRangePadding -> Automatic, PlotRegion -> Automatic,
PreserveImageOptions -> Automatic, Prolog -> {},
RotationAction -> "Fit", SphericalRegion -> True, Ticks -> None,
TicksStyle -> {}, TouchscreenAutoZoom -> False,
ViewAngle -> 0.33632810973764027`,
ViewCenter -> {0.5`, 0.5`, 0.5`}, ViewMatrix -> Automatic,
ViewPoint -> {-1.9461497767487252`, 1.477527579217831`,
2.340814665690469`}, ViewProjection -> Automatic,
ViewRange -> All, ViewVector -> Automatic,
ViewVertical -> {0.23556268765910476`, -0.24706981260320413`,
0.9399291079028442`}]}}]
``````

Which gives:

Scaling does not solve this problem.