Magnification factors for macro lenses

[dobbino]

Hi folks,

First post!

As part of this article: https://www.cambridgeincolour.com/tu...cro-lenses.htm, there is a magnification factor calculator. I am using a Canon 100ml macro lens, and the closest focusing distance is 300mm. However, when I use the 300mm measurement in the calculator, I get a message which reads "Focusing distance must be at least four times the focal length". I'm probably overlooking something obvious, but just don't understand. If someone can enlighten me I would be most grateful.

Thanks and bests,
Rob.

[Manfred M]

Welcome to CiC, Rob. Would you mind clicking the "My Profile" button on the top of this page and adding your first name and where you are from to your profile setting? That just makes it a bit easier for this information to follow you around on your postings here. We are a fairly informal group here at CiC and tend to go on a first name basis.

With regard to your question, I suspect that the reason you are getting the error is that you are likely inputting the incorrect distance into the lens calculator. The focusing distance in the calculator requires the subject to sensor plane distance. Most people measure from the subject to the front element of the lens, and this is not what the calculator is looking for.

[dobbino]

Hi Manfred - thanks for your response. I think I do have my calculations correct, however. This is from the Lens Instruction Manual: Closeup Photography
Close-up photos up to 1x (life-size) magnification
are possible. The minimum focusing distance of
30 cm is the distance from the subject to the
focal plane. The working distance from the front
of the lens to the subject is about 14 cm

[george013]

Doing macro, magnification, the distance to the film/sensor plane is used. There's a mark on the camera from which one can measure.
But with the dof-calculator the distance from the optical center is meant.

So in the tut a distance of 300mm and a focal length of 75 gives a magnification of 1, 150mm before the optical center and 150mm behind the optical center.

George

[Manfred M]

Hi Manfred - thanks for your response. I think I do have my calculations correct, however. This is from the Lens Instruction Manual: Closeup Photography
Close-up photos up to 1x (life-size) magnification
are possible. The minimum focusing distance of
30 cm is the distance from the subject to the
focal plane. The working distance from the front
of the lens to the subject is about 14 cm

In that case, you have a system the exceeds the CiC's macro calculators range.

[DanK]

I suspect the answer is that the functional focal length of macro lenses at minimum focusing distance is typically less than the nominal focal length because of the movement of the lens elements when focusing close. I haven't paid much attention to this in a long time, as I haven't had reason to worry about it in doing my macro work, but if you google, you can probably find something.

[dem]

Hi Rob. This calculator seems to think that 1:1 magnification ratio is as much as you can possibly get from a macro lens. When the focusing distance is 4 times the focal length, you get 1:1 magnification. Obviously there are lenses that can do better than 1:1.

There is nothing special about 1:1 magnification apart from a catchy name.

If I were you I would just take a shot of a ruler at the minimum focus distance. You know what the width of your sensor is, you can work out the magnification ratio yourself.

The problem with the calculator is that it does not know anything about "focus breathing" that depends on the lens design. A 100 mm lens is a 100 mm lens only when focused on infinity. Focus it on a nearby object and the actual focus lenght will get shorter.

[dobbino]

Hi George - thanks for your input, but it doesn't really help as the focal length of my lens is 100mm, not 75mm, so the calculator throws out the error message. Anyway, in practice I am just dividing the height of my sensor (24mm) by the height of the subject to estimate the magnification factor.

[dobbino]

Thanks dem - appreciated. Makes sense.

[dobbino]

Thanks Dan.

[dobbino]

Lol - thanks!

[george013]

Hi George - thanks for your input, but it doesn't really help as the focal length of my lens is 100mm, not 75mm, so the calculator throws out the error message. Anyway, in practice I am just dividing the height of my sensor (24mm) by the height of the subject to estimate the magnification factor.

I don't understand you. The calculator has only 3 fields. You can set the unit, in this case mm, you can set the focal length, and you can set the focal distance which has to be minimal 4 times the focal length. If you use 100mm and 400mm and press calculate the answer is 1.

For some reason the calculator doesn't go further as a magnification of 1.

If you look at the specs of your lens and read the minimal distance and you divide that through 4, than you have the actual focal length of that lens at the shortest object distance. I know the Nikon105 Macro becomes something of 75, but with a magnification of 1.

I just read the min. focus distance of the Canon 100mm macro is 300mm with a magnification of 1. Seeing those figures it's measured from the film plane, and that means the lens becomes a 75 mm lens.

George

[William W]

The “4 times” formula is only correct for a Single Element Lens.

The EF 100mm F/2.8 Macro has 12 Elements in 8 Groups and therefore that formula is invalid.

There is (complicated) Mathematics to arrive at the appropriate formula to use, however: if the lens actually produces x1 Magnification (i.e. 1:1), then the simplest, correct formula to find the EFFECTIVE Focal Length is 1/2 of the WORKING Distance (Subject to Front Nodal Point).

I understand that the Minimum Working Distance for the EF 100 F/2.8 lens is 149mm:
Hence 149/2 = 74.5mm

On the other hand, we can use the "4 times rule" to calculate the EFFECTIVE Focal Length when we know the Minimum Focus Distance (Subject to Film Plane) and we also assume that the Lens is truly 1:1 at that MFD.

I understand the Minimum Focus Distance is 310mm, so we could just divide that by 4 . . . 77.5mm

I think we’re pretty close to the EFFECTIVE Focal Length, either way.

If the truth be known the lens might actually be a smidge less than 1:1

WW

[dobbino]

I don't understand you. The calculator has only 3 fields. You can set the unit, in this case mm, you can set the focal length, and you can set the focal distance which has to be minimal 4 times the focal length. If you use 100mm and 400mm and press calculate the answer is 1.

For some reason the calculator doesn't go further as a magnification of 1.

If you look at the specs of your lens and read the minimal distance and you divide that through 4, than you have the actual focal length of that lens at the shortest object distance. I know the Nikon105 Macro becomes something of 75, but with a magnification of 1.

I just read the min. focus distance of the Canon 100mm macro is 300mm with a magnification of 1. Seeing those figures it's measured from the film plane, and that means the lens becomes a 75 mm lens.

George

Hi again George - looking back at my original post, I probably didn't explain myself as clearly as I should have. When I said I received an error message saying "Focusing distance must be at least four times the focal length", and that I didn't understand - I meant I didn't understand why the focusing distance must be at least four times the focal length. Please - I don't want you to waste any more of your time and I thank you for your trouble - but where the factor of 4 comes in is still a mystery. I have Googled the issue but haven't found a satisfactory explanation. But I'm not fussed as I can get what I need as mentioned above. Thanks again.

[dobbino]

Hi William - thanks very much for your time. The maths and the "4 times rule" are unfortunately a little out of the range of my technically challenged brain I'm afraid. I understand about dividing by 4, etc., just don't understand where the "4" comes in. But you guys have spent enough time on the subject, and I really am most appreciative.

[george013]

The “4 times” formula is only correct for a Single Element Lens.

The EF 100mm F/2.8 Macro has 12 Elements in 8 Groups and therefore that formula is invalid.

There is (complicated) Mathematics to arrive at the appropriate formula to use, however: if the lens actually produces x1 Magnification (i.e. 1:1), then the simplest, correct formula to find the EFFECTIVE Focal Length is 1/2 of the WORKING Distance (Subject to Front Nodal Point).

I understand that the Minimum Working Distance for the EF 100 F/2.8 lens is 149mm:
Hence 149/2 = 74.5mm

On the other hand, we can use the "4 times rule" to calculate the EFFECTIVE Focal Length when we know the Minimum Focus Distance (Subject to Film Plane) and we also assume that the Lens is truly 1:1 at that MFD.

I understand the Minimum Focus Distance is 310mm, so we could just divide that by 4 . . . 77.5mm

I think we’re pretty close to the EFFECTIVE Focal Length, either way.

If the truth be known the lens might actually be a smidge less than 1:1

WW

Quite a difficult way to come to the same result.
The minimum focus distance is 300mm as said in the opening post and by Canon, if we're talking of the same lens. https://www.usa.canon.com/internet/p...l-macro-is-usm

George

[xpatUSA]

Hi William - thanks very much for your time. The maths and the "4 times rule" are unfortunately a little out of the range of my technically challenged brain I'm afraid. I understand about dividing by 4, etc., just don't understand where the "4" comes in. But you guys have spent enough time on the subject, and I really am most appreciative.

Here you go, Rob, a simple diagram of a 1:1 situation which explains the 4X "rule":



The arrow object is the same size as the arrow image, by the definition of 1:1. By geometry (similar triangles) that means that the object must be the same distance from the lens as the image is from the lens. Now we look at the two rays, starting with the one on top that enters the lens horizontally. We know that the lens will bend that ray so that it passes through the lens's marked focal length shown above as 'f'. As you can see, 'f' is halfway between the lens and the sensor, therefore the lens (for 1:1) is 2X the focal length away from the sensor. And if the object must be the same distance from the lens as the image is from the lens, that adds up to the object being 4X the marked focal length away from the sensor (a.k.a. the image plane, i.e. the little circle with a line through it, marked on your camera body somewhere).

The other ray just confirms that the set-up is indeed 1:1 . . .

[William W]

Here you go, Rob . . .

Beat me to it.

WW

[William W]

Quite a difficult way to come to the same result . . .

Um no???

I don't think that is difficult at all.

I provided two different simple formulae

The first one is the same yours:

If we assume that the data of the lens manufacturer is correct and the Lens does provide 1:1, then all we need to know is the Minimum Focus Distance and we divide that by 4 and that will produce the EFFECTIVE Focal Length of the Macro Lens at the Minimum Focus Distance.

However, the question was not really about that, but rather it was about the CiC calculator which requires the Focal Length data to be inputted (more correctly NOT the NOMINAL Focal Length but the EFFECTIVE Focal Length) and Rob was asking why the CiC Calculator was not working for him and the answer is because he was not putting in the correct Focal Length, so, logically Rob needed to find out HOW to get the correct Focal Length. That can be achieved if we know the MINIMUM WORKING DISTANCE. The MWD can be measured by observation or found in some data sheets.

For the EF 100 F/2.8 USM, I understand that the MWD is 149mm, hence we can compute (not difficult to divide by 2) that the EFFECTIVE Focal Length when the lens is at MWD (and thus also at MFD) is 74.5mm. . .

So if we then go back the CiC Calculator and plonk in 310mm for the MWD and 74.5mm for the Focal Length we get an answer the lens has a Magnification x 0.67 . . .

IF the lens does produce 1:1 then those mm dimension quoted on the data sheets are minutely in error. I note that Lens' Manufactures' DATA SHEETS are sometimes "close enough".

*

The Lens cited in the OP (I assumed) is the EF 100 F/2.8 USM

Note that there are three (3) Canon 100mm F/2.8 Macro Lenses in the "EF Series", none of which share the same elements and lens' groupings. I don't know off the top of my head without checking my data file what the MFD is for the three but I do know that the MFD (as stated in Canon data) for the EF 100 F/2.8 USM is 310mm.

I own this lens: if I have time latter today I will do a lab test.

WW

[William W]

UPDATE AND (maybe) CORRECTION - depending upon what ens it is that Rob has . . .


I just re-read the OP. Excerpt here -

I am using a Canon 100ml macro lens . . .

I originally thought that was a typo meaning "EF 100mm F/2.8 USM" but I think it now is a typo meaning "EF 100 F/2.8 L IS USM"

If Rob has the latter lens then, yes, the data sheets state that the MFD for that lens is 300mm (not 310mm as I stated assuming a different lens).

From my diary notes when I tested the EF 100 F/2.8 L IS USM, the MWD data stated was 144mm, (i.e. NOT 149mm as per my EF 100 F/2.8 USM).

That means the EFFECTIVE Focal Length at the Maximum Magnification for the EF 10 F/2.8 L IS USM is about 72mm.

Hence putting those figures into the CiC calculator we get a magnification = x 0. 67 (again!).

If I get the time I will still do a rough lab test on my own lens: as mentioned previously the Canon Data Sheets are probably in error by a couple of mm and that is enough to throw the calculator (or the user of the calculator) into an (unnecessary) meltdown.

***

Rob,

You can do a really easy and very simple test yourself to clear up any fears or reservations that you might have about your lens: simply get a bit of 1mm graph paper (or any paper) and draw a rectangle 24mm (h) x 36mm (w) and maybe colour it in, if you do not have graph paper.

Then get your 100mm Macro Lens (which ever one it is) and set it to the closest focus distance and then creep up on the rectangle and make a picture when it is in precise focus . . . (please use a 135 Format camera)

a) if the rectangle sits EXACTLY in your image file's frame - then you have 1:1
b) if the rectangle spills over the edge of your image file's frame - then you have greater than 1:1
c) if the rectangle has the outside showing in the your image file's frame - then you have less than 1:1

WW

POST SCRIPT: I did the exercise as an example for you and anyone else interested in checking their own macro lens - see my comment #21 below . . .