40-150 PRO focus breathing?

[Arctra]

Today my Olympus 40-150 PRO lens arrived and while it does feel like a great lens, there's something that I noticed. I was comparing it against my trusty old Minolta Beercan and I was noticing that the Olympus zoomed all the way in at 150mm was producing a similar result as the Beercan at 210mm.

I ran the test again, but this time with APS-C crop mode turned on my Sony cam to simulate ~300ishmm and I had to get significantly closer to my test subject (in this case a old Charmander piggy bank) with the Oly to produce a similar FOV. This isn't a deal-breaking issue for me but it wasn't something I was expecting to see as I hadn't seen any reports of focus breathing issues with this lens.

Is this something that is known about this lens? Is mine the special one on the block? Or am I just fundamentally misunderstanding equivalency here? Like I said, not a huge deal-breaker but was definitely interesting to see.

 

[CrisPhoto]

...

It's very easy to calculate the focus breathing from the lens specs. The 40-150 PRO has a max reproduction ratio of 0.21 (at 150 mm obviously) and a minimum focus distance of 0.7 meters. The focal length, F, at that reproduction ratio, R, and focus distance, D, is calculated as

F = D/(1/R + R + 2) = 700/(1/0.21 + 0.21 + 2) = 100 mm

so yes, certainly some focus breathing going on, just as one might expect.

...

I took Anders formula, the manufacturers specs and checked it against reality. I put the camera on a tripod, took two folding rulers: one as subject to get the FOV in mm and the other to get the distance as well as the working distance.

Here is my excel sheet:


Spec values against real values and AndersW's formula (effective focal length)

I think the 40-150 PRO does quite well.

The 12-40 was a nice surprise, it does equally well. But the working distance is 8x smaller. Not good for butterflies and such ...

The PanaLeica has a lot of focus breathing but at least the result is as crispy as the PRO lenses, despite the bad numbers it is very usable for close up.

And the small 40-150/5.6 was very disappointing. Two years ago I used it for close up and macro, how much better would the PRO lenses have been :-(

This is the thing the table does not tell: with the PL14-150 as the only exception the non-PRO lenses give up IQ very dramatically if you go closer. Sharpness and contrast is going down the drain ...

Christof

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[Anders W]

...

It's very easy to calculate the focus breathing from the lens specs. The 40-150 PRO has a max reproduction ratio of 0.21 (at 150 mm obviously) and a minimum focus distance of 0.7 meters. The focal length, F, at that reproduction ratio, R, and focus distance, D, is calculated as

F = D/(1/R + R + 2) = 700/(1/0.21 + 0.21 + 2) = 100 mm

so yes, certainly some focus breathing going on, just as one might expect.

...

I took Anders formula, the manufacturers specs and checked it against reality. I put the camera on a tripod, took two folding rulers: one as subject to get the FOV in mm and the other to get the distance as well as the working distance.

Here is my excel sheet:


Spec values against real values and AndersW's formula (effective focal length)

I think the 40-150 PRO does quite well.

The 12-40 was a nice surprise, it does equally well. But the working distance is 8x smaller. Not good for butterflies and such ...

The PanaLeica has a lot of focus breathing but at least the result is as crispy as the PRO lenses, despite the bad numbers it is very usable for close up.

And the small 40-150/5.6 was very disappointing. Two years ago I used it for close up and macro, how much better would the PRO lenses have been :-(

This is the thing the table does not tell: with the PL14-150 as the only exception the non-PRO lenses give up IQ very dramatically if you go closer. Sharpness and contrast is going down the drain ...

Hi Christof,

Thanks for that. Quite an ambitious little exercise. Much appreciated.

Note, however, that the figures for the 75-300 are not right. This lens manages a focus distance of 0.9 meters only at 75 mm. At any other focal length, the minimum focus distance, is 1.5 meters. At 300 mm, which is where it manages a reproduction ratio of 0.18, its effective focal length is 194 mm, not 116 mm. And are you sure its MTF-values too are going down the drain at close distance? I haven't really tried to test it but ...

 

[RichRMA]

.

 

[CrisPhoto]

...

Hi Christof,

Thanks for that. Quite an ambitious little exercise. Much appreciated.

Note, however, that the figures for the 75-300 are not right. This lens manages a focus distance of 0.9 meters only at 75 mm. At any other focal length, the minimum focus distance, is 1.5 meters. At 300 mm, which is where it manages a reproduction ratio of 0.18, its effective focal length is 194 mm, not 116 mm. And are you sure its MTF-values too are going down the drain at close distance? I haven't really tried to test it but ...

Hello Anders,

thanks for the hint, here the updated table. sorted by magnification "R":


Corrected table, real and measured specs

The 40-150 PRO lens has spoiled me, this little wonderful jewel works very reliable from macro close-up to tele. Made it very difficult for me to buy a walk around lens this year, hard to take a step back regarding IQ.

Here is a fast comparison of 40-150 PRO, Panasonic 14-140 II, Olympus 40-150 I and the PanaLeica 14-150:


This is the scene captured by the P 14-140 II, you can see the loss of detail and the weak color contrast even in this smallish screen shot




This a 100% crop of the scene above. (improved version with less dramatic difference, sorry, first version of this crop was not on the focus plane which was not on favor for the 10x zooms)



These were shot from a good tripod (I have a better one now), hand held the decrease of sharpness would have been even worse ...

Regards

Christof

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[Martin.au]

...

It's very easy to calculate the focus breathing from the lens specs. The 40-150 PRO has a max reproduction ratio of 0.21 (at 150 mm obviously) and a minimum focus distance of 0.7 meters. The focal length, F, at that reproduction ratio, R, and focus distance, D, is calculated as

F = D/(1/R + R + 2) = 700/(1/0.21 + 0.21 + 2) = 100 mm

so yes, certainly some focus breathing going on, just as one might expect.

...

I took Anders formula, the manufacturers specs and checked it against reality. I put the camera on a tripod, took two folding rulers: one as subject to get the FOV in mm and the other to get the distance as well as the working distance.

Here is my excel sheet:


Spec values against real values and AndersW's formula (effective focal length)

I think the 40-150 PRO does quite well.

The 12-40 was a nice surprise, it does equally well. But the working distance is 8x smaller. Not good for butterflies and such ...

The PanaLeica has a lot of focus breathing but at least the result is as crispy as the PRO lenses, despite the bad numbers it is very usable for close up.

And the small 40-150/5.6 was very disappointing. Two years ago I used it for close up and macro, how much better would the PRO lenses have been :-(

This is the thing the table does not tell: with the PL14-150 as the only exception the non-PRO lenses give up IQ very dramatically if you go closer. Sharpness and contrast is going down the drain ...

Christof

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

Chuck a macro in as well. That's a good way to check the maths. Good work.

 

[CrisPhoto]

...

Chuck a macro in as well. That's a good way to check the maths. Good work.

Good point.

i skipped the macro as it is a prime lens. But you are right, focus breathing is not limited to zoom lenses at all.

Therefore, the updated table:


Adde the 60mm macro, as expected, it is the new number one in our little chart

From the numbers,the macro lens seems to have 22% focus breathing.

But a quick focus test is showing me that the background is growing 30% when I focus from 30cm to 10cm. This would be -30% focus breathing in our table, isn't it? Confusing ...

Christof

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[whumber]

From the numbers,the macro lens seems to have 22% focus breathing.

But a quick focus test is showing me that the background is growing 30% when I focus from 30cm to 10cm. This would be -30% focus breathing in our table, isn't it? Confusing ...

Like I said earlier in the thread, the equation Anders used is only valid when the thin lens assumption is valid, or to put it another when the distance between the principle planes is much less than the subject distance. For some lenses this can be a reasonable assumption, but it's not reasonable in any general sense.

 

[Anders W]

Today my Olympus 40-150 PRO lens arrived and while it does feel like a great lens, there's something that I noticed. I was comparing it against my trusty old Minolta Beercan and I was noticing that the Olympus zoomed all the way in at 150mm was producing a similar result as the Beercan at 210mm.

I ran the test again, but this time with APS-C crop mode turned on my Sony cam to simulate ~300ishmm and I had to get significantly closer to my test subject (in this case a old Charmander piggy bank) with the Oly to produce a similar FOV. This isn't a deal-breaking issue for me but it wasn't something I was expecting to see as I hadn't seen any reports of focus breathing issues with this lens.

Is this something that is known about this lens? Is mine the special one on the block? Or am I just fundamentally misunderstanding equivalency here? Like I said, not a huge deal-breaker but was definitely interesting to see.

It's very easy to calculate the focus breathing from the lens specs. The 40-150 PRO has a max reproduction ratio of 0.21 (at 150 mm obviously) and a minimum focus distance of 0.7 meters. The focal length, F, at that reproduction ratio, R, and focus distance, D, is calculated as

F = D/(1/R + R + 2) = 700/(1/0.21 + 0.21 + 2) = 100 mm

so yes, certainly some focus breathing going on, just as one might expect.

This equation is based on a thin lens model and while it may be fairly accurate at infinity focus, it's going to fall apart at close focus distances with thick lenses (i.e. any real lens you can imagine), especially for a lens where the distance between the principal planes is on the order of 10% of the subject distance.

I am well aware that it is based on a thin lens model but that doesn't make it useless for the purpose at hand. Moreover, the formula is useful precisely at close focus distances. At infinity, there is no real need for it.

I think that tells you a lot about the usefulness of that equation for your intended purpose. For some lenses that have principle planes relatively close together and have a long MFD, the equation may be somewhat useful, but for a lens like the 40-150 it completely falls apart. If you want another example where your formula is not useful, look at the Canon 70-200ii. The thin lens approximation equation would suggest that the focal length at MFD decreases to somewhere around 176mm, while direct measurements show that the focal length actual increases to well above 200mm at MFD.

What the results of the formula tells us is that the focal length of the 40-150 when set to 150 mm and shot at its minimum focus distance is equivalent to that of a thin lens (a single lens element) with a focal length of 100 mm. If there were no focus breathing, it would instead be equivalent to a thin lens with a focal length of 150 mm (provided that the 150 mm specification is correct in the first place).

I'm sorry but you're just flat out wrong on this one. The focal length of the 40-150 is nowhere close to 100mm at MFD when set to 150mm. In fact, there's almost no change in focal length at 150mm between infinity and MFD. Below are shots of a test target taken with the 40-150 @ 150mm with the focus set to infinity and MFD. If the thin lens approximation was reasonable, we would see a siginificant decrease in the target size. Instead what we see is almost zero change in the target size, at least to within the precision that the out of focus target will allow us.


Infinity Focus | f/22 | Subject Distance ~8ft


MFD Focus | f/22 | Subject Distance ~8ft

I think the problem is basically that we are talking past each other rather than substantively disagreeing. Let me try to clarify what I am and am not trying to say.

What I am trying to say is that the 40-150/2.8 set to 150 mm and shot at its miniumum focus distance has a reproduction ratio, and thus a field of view (expressed in linear rather than angular terms, e.g. in millimeter à la Christof/CrisPhoto), that is identical to that of a thin lens with a focal length of 100 mm shot at the same focus distance. It also has a reproduction ratio/linear FoV at those settings that is approximately (but not exactly) the same as that of an old-fashioned, reasonably symmetric 100 mm lens that focuses by moving the entire array of lens elements in and out, without any use of floating elements.

What I am not trying to say is that either a thin lens with an FL of 100 mm or the 40-150/2.8 set to 150 mm has an effective focal length of 100 mm with both shot at a focus distance of 0.7 meters. If we define the effective focal length of lens X shot at focus distance Y as the focal length of a lens that gives the same angle of view as X shot at Y when shot at infinity, then the effective focal length of the thin 100 mm lens at 0.7 meters is F(1 + R) = 100(1 + 0.21) = 121 mm. For a thick and potentially asymmetric lens like the 40-150/2.8 set to 150 mm and 0.7 meters, the effective focal length instead becomes F(1 + R/P) where P is the pupil magnification (the ratio of the diameter of the exit pupil to the entrance pupil). But since I don't know what F and P are in this case, I can't calculate the result.

Since the effective focal length is what determines the angle of view, it follows from the above that a thin lens gets a narrower field of view at short focus distances than at infinity. The same is true about an old-fashioned lens of the kind I described above. Your experiment indicates that this is not the case for the 40-150/2.8 set to 150 mm. Instead, its fairly constant angle of view suggests that its effective focal length doesn't change much as you go from infinity focus to minimum focus distance but that the focal length, F, declines (since R/P surely increases).

 

[Anders W]

...

Hi Christof,

Thanks for that. Quite an ambitious little exercise. Much appreciated.

Note, however, that the figures for the 75-300 are not right. This lens manages a focus distance of 0.9 meters only at 75 mm. At any other focal length, the minimum focus distance, is 1.5 meters. At 300 mm, which is where it manages a reproduction ratio of 0.18, its effective focal length is 194 mm, not 116 mm. And are you sure its MTF-values too are going down the drain at close distance? I haven't really tried to test it but ...

Hello Anders,

thanks for the hint, here the updated table. sorted by magnification "R":


Corrected table, real and measured specs

A couple of more things about the table now that I have had the time to digest it more carefully.

1. There is a similar issue with the 14-140 II as with the 75-300 (different minimum focus distance at different FLs). The 14-140 II manages 0.3 meters at 14-21 mm only. For the rest of the range, the minimum focus distance is 0.5 meters, in line with your findings in the penultimate column.

2. I can't get the reproduction ratios in the table to square fully with the FoV figures. I assume the FoVs are horizontal FoVs. If so a reproduction ratio of 0.30 corresponds to an FoV of 17.3 mm (the width of an MFT sensor) divided by 0.3, which is 57.67 mm rather than 60 mm. It seems like you have calculated with a sensor width of 18 mm instead of 17.3. With the correct sensor width, the figures in the "FoV" and "Real FoV" columns as well as those in the "Ratio" and "Real Ratio" columns (the latter of which need correction just like those in the "FoV" column), will be a bit closer to one another.

3. The focal lengths you calculated by means of the formula for a thin lens that I provided shouldn't be labeled "effective focal length". Although I understand why you label it like that, the term "effective focal length" is already occupied for slightly different purposes (see my reply to whumber here). What the formula I provided gives you is the focal length of a thin lens having the same reproduction ratio and linear FoV as the target lens when both are shot at the minimum focus distance of the target lens.

The 40-150 PRO lens has spoiled me, this little wonderful jewel works very reliable from macro close-up to tele. Made it very difficult for me to buy a walk around lens this year, hard to take a step back regarding IQ.

Although I have no personal experience with the 40-150/2.8 yet, I can certainly understand the feeling.

Here is a fast comparison of 40-150 PRO, Panasonic 14-140 II, Olympus 40-150 I and the PanaLeica 14-150:

I see what you are talking about. But I don't think the results from 14-140 II and 40-150/4-5.6 are all that shabby. And are you sure that the performance difference has much to do with the close focus? Wouldn't we see similar differences at other distances too?

This is the scene captured by the P 14-140 II, you can see the loss of detail and the weak color contrast even in this smallish screen shot


This a 100% crop of the scene above. (improved version with less dramatic difference, sorry, first version of this crop was not on the focus plane which was not on favor for the 10x zooms)

These were shot from a good tripod (I have a better one now), hand held the decrease of sharpness would have been even worse ...

Regards

Christof

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[Anders W]

...

Chuck a macro in as well. That's a good way to check the maths. Good work.

Good point.

i skipped the macro as it is a prime lens. But you are right, focus breathing is not limited to zoom lenses at all.

Therefore, the updated table:


Adde the 60mm macro, as expected, it is the new number one in our little chart

From the numbers,the macro lens seems to have 22% focus breathing.

But a quick focus test is showing me that the background is growing 30% when I focus from 30cm to 10cm. This would be -30% focus breathing in our table, isn't it? Confusing ...

If by "growing" you mean that the background is magnified more as you reduce the focus distance, it is not really confusing if you consider what I say in my reply to whumber here. As I pointed out in my earlier reply to you here, the formula I provided gives you the focal length of a thin lens having the same reproduction ratio and linear FoV as the target lens when both are shot at the minimum focus distance of the target lens. But a thin lens with a focal length of 47 mm has an effective focal length (see my reply to whumber here for the conventional definition of "effective focal length"), when shot at a focus distance of 188 mm of 47(1 + R) = 47(1 + 1) = 94 mm, and the effective focal length is what determines the angle of view. So it is not surprising that the 60/2.8 macro gets a more narrow AoV as you reduce the focus distance in spite of the fact that its focal length stays more or less constant.

 

[whumber]

I think the problem is basically that we are talking past each other rather than substantively disagreeing. Let me try to clarify what I am and am not trying to say.

You're correct, I was misunderstanding what you were trying to say.

What I am trying to say is that the 40-150/2.8 set to 150 mm and shot at its miniumum focus distance has a reproduction ratio, and thus a field of view (expressed in linear rather than angular terms, e.g. in millimeter à la Christof/CrisPhoto), that is identical to that of a thin lens with a focal length of 100 mm shot at the same focus distance. It also has a reproduction ratio/linear FoV at those settings that is approximately (but not exactly) the same as that of an old-fashioned, reasonably symmetric 100 mm lens that focuses by moving the entire array of lens elements in and out, without any use of floating elements.

What I am not trying to say is that either a thin lens with an FL of 100 mm or the 40-150/2.8 set to 150 mm has an effective focal length of 100 mm with both shot at a focus distance of 0.7 meters. If we define the effective focal length of lens X shot at focus distance Y as the focal length of a lens that gives the same angle of view as X shot at Y when shot at infinity, then the effective focal length of the thin 100 mm lens at 0.7 meters is F(1 + R) = 100(1 + 0.21) = 121 mm. For a thick and potentially asymmetric lens like the 40-150/2.8 set to 150 mm and 0.7 meters, the effective focal length instead becomes F(1 + R/P) where P is the pupil magnification (the ratio of the diameter of the exit pupil to the entrance pupil). But since I don't know what F and P are in this case, I can't calculate the result.

Ok, I'm in complete agreement with everything here. I think the only thing we (maybe?) disagree on is that the relationship initially posted is not very useful at close focus distances, at least not in a very general sense.

I am well aware that it is based on a thin lens model but that doesn't make it useless for the purpose at hand. Moreover, the formula is useful precisely at close focus distances.

If it was just a matter of it being off a bit, then that would be one thing but you can easily end up in situations where it's not even giving you the right trend depending on the lens design. Again though, I think maybe I'm misunderstanding your intention here.

 

[CrisPhoto]

...

If by "growing" you mean that the background is magnified more as you reduce the focus distance, it is not really confusing if you consider what I say in my reply to whumber here. As I pointed out in my earlier reply to you here, the formula I provided gives you the focal length of a thin lens having the same reproduction ratio and linear FoV as the target lens when both are shot at the minimum focus distance of the target lens. But a thin lens with a focal length of 47 mm has an effective focal length (see my reply to whumber here for the conventional definition of "effective focal length"), when shot at a focus distance of 188 mm of 47(1 + R) = 47(1 + 1) = 94 mm, and the effective focal length is what determines the angle of view. So it is not surprising that the 60/2.8 macro gets a more narrow AoV as you reduce the focus distance in spite of the fact that its focal length stays more or less constant.

Hi again,

thanks for the good reading. As a good guy, I have updated the table slightly (17,3mm width instead of 18, thin lens instead of effective)





Regarding the sharpness loss, last time I browsed my photos very fast and took a bad example (different focal plane and not very close).



If you would go closer, the differences get more obvious, to the point that you realize the missing sharpness in the EVF. In the next sample I went as close as I could (R=0.2) and took the Oly 14-150 shot three times because I could not believe how bad it was ...


Close up near maximum magnification of 0.2



--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[CrisPhoto]

Here is another example with more contrast/more colors:





--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[dennis tennis]

I think the problem is basically that we are talking past each other rather than substantively disagreeing. Let me try to clarify what I am and am not trying to say.

You're correct, I was misunderstanding what you were trying to say.

What I am trying to say is that the 40-150/2.8 set to 150 mm and shot at its miniumum focus distance has a reproduction ratio, and thus a field of view (expressed in linear rather than angular terms, e.g. in millimeter à la Christof/CrisPhoto), that is identical to that of a thin lens with a focal length of 100 mm shot at the same focus distance. It also has a reproduction ratio/linear FoV at those settings that is approximately (but not exactly) the same as that of an old-fashioned, reasonably symmetric 100 mm lens that focuses by moving the entire array of lens elements in and out, without any use of floating elements.

What I am not trying to say is that either a thin lens with an FL of 100 mm or the 40-150/2.8 set to 150 mm has an effective focal length of 100 mm with both shot at a focus distance of 0.7 meters. If we define the effective focal length of lens X shot at focus distance Y as the focal length of a lens that gives the same angle of view as X shot at Y when shot at infinity, then the effective focal length of the thin 100 mm lens at 0.7 meters is F(1 + R) = 100(1 + 0.21) = 121 mm. For a thick and potentially asymmetric lens like the 40-150/2.8 set to 150 mm and 0.7 meters, the effective focal length instead becomes F(1 + R/P) where P is the pupil magnification (the ratio of the diameter of the exit pupil to the entrance pupil). But since I don't know what F and P are in this case, I can't calculate the result.

Ok, I'm in complete agreement with everything here. I think the only thing we (maybe?) disagree on is that the relationship initially posted is not very useful at close focus distances, at least not in a very general sense.

I am well aware that it is based on a thin lens model but that doesn't make it useless for the purpose at hand. Moreover, the formula is useful precisely at close focus distances.

If it was just a matter of it being off a bit, then that would be one thing but you can easily end up in situations where it's not even giving you the right trend depending on the lens design. Again though, I think maybe I'm misunderstanding your intention here.

have to jump in a say, a rare thing for my posts, glad you guys ended up agreeing.

Also, the Canon 70-200mk2 is a rare zoom lens to have so little focus breathing at 200mm and yet be IF and have the same size and weight as its competition.

 

[Anders W]

...

If by "growing" you mean that the background is magnified more as you reduce the focus distance, it is not really confusing if you consider what I say in my reply to whumber here. As I pointed out in my earlier reply to you here, the formula I provided gives you the focal length of a thin lens having the same reproduction ratio and linear FoV as the target lens when both are shot at the minimum focus distance of the target lens. But a thin lens with a focal length of 47 mm has an effective focal length (see my reply to whumber here for the conventional definition of "effective focal length"), when shot at a focus distance of 188 mm of 47(1 + R) = 47(1 + 1) = 94 mm, and the effective focal length is what determines the angle of view. So it is not surprising that the 60/2.8 macro gets a more narrow AoV as you reduce the focus distance in spite of the fact that its focal length stays more or less constant.

Hi again,

thanks for the good reading. As a good guy, I have updated the table slightly (17,3mm width instead of 18, thin lens instead of effective)



Regarding the sharpness loss, last time I browsed my photos very fast and took a bad example (different focal plane and not very close).

If you would go closer, the differences get more obvious, to the point that you realize the missing sharpness in the EVF. In the next sample I went as close as I could (R=0.2) and took the Oly 14-150 shot three times because I could not believe how bad it was ...

Thanks! That's certainly a convincing illustration.

Close up near maximum magnification of 0.2

--
OM-D + Sam7.5, O25, O60, O75
O12-40, O40-150, P 14-140

 

[Anders W]

I think the problem is basically that we are talking past each other rather than substantively disagreeing. Let me try to clarify what I am and am not trying to say.

You're correct, I was misunderstanding what you were trying to say.

No problem. I realize that what I said is subject to more than one reasonable interpretation.

What I am trying to say is that the 40-150/2.8 set to 150 mm and shot at its miniumum focus distance has a reproduction ratio, and thus a field of view (expressed in linear rather than angular terms, e.g. in millimeter à la Christof/CrisPhoto), that is identical to that of a thin lens with a focal length of 100 mm shot at the same focus distance. It also has a reproduction ratio/linear FoV at those settings that is approximately (but not exactly) the same as that of an old-fashioned, reasonably symmetric 100 mm lens that focuses by moving the entire array of lens elements in and out, without any use of floating elements.

What I am not trying to say is that either a thin lens with an FL of 100 mm or the 40-150/2.8 set to 150 mm has an effective focal length of 100 mm with both shot at a focus distance of 0.7 meters. If we define the effective focal length of lens X shot at focus distance Y as the focal length of a lens that gives the same angle of view as X shot at Y when shot at infinity, then the effective focal length of the thin 100 mm lens at 0.7 meters is F(1 + R) = 100(1 + 0.21) = 121 mm. For a thick and potentially asymmetric lens like the 40-150/2.8 set to 150 mm and 0.7 meters, the effective focal length instead becomes F(1 + R/P) where P is the pupil magnification (the ratio of the diameter of the exit pupil to the entrance pupil). But since I don't know what F and P are in this case, I can't calculate the result.

Ok, I'm in complete agreement with everything here. I think the only thing we (maybe?) disagree on is that the relationship initially posted is not very useful at close focus distances, at least not in a very general sense.

I am well aware that it is based on a thin lens model but that doesn't make it useless for the purpose at hand. Moreover, the formula is useful precisely at close focus distances.

If it was just a matter of it being off a bit, then that would be one thing but you can easily end up in situations where it's not even giving you the right trend depending on the lens design. Again though, I think maybe I'm misunderstanding your intention here.

I was only trying to offer an analogy (as outlined in the paragraph that begins with "What I am trying to say") that might be helpful to at least some readers. But as suggested by the paragraphs that follow, no simple analogy works in all respects. And in view of that, I am not sure how much it helps to bring focal length into the picture in the first place.

If we consider things from a practical photographic point of view, I'd say that there are two sets of parameters that are of primary interest in this context. The first is how high a reproduction ratio you can get and at what working distance (distance from the subject to the tip of the lens). The reproduction ratio is part of the lens specs and the working distance can be calculated from the specs (minium focus distance minus the flange distance and the length of the lens), although in some cases you may need to look at pictures of the lens in order to see how much its length increases when zooming in (for zoom lenses without internal zooming) and/or focusing close (for lenses without internal focus).

But although it is nice (at least I think so) to get as high a reproduction ratio along with as long a working distance as possible, there is also another couple of parameters to consider, namely the extent to which the angle of view and the location of the entrance pupil stay constant when you change the focus distance. For maximum ease of composition/framing and for the best results in focus stacking you wouldn't want either of them to change with the focus distance. But regrettably, it is not so easy to tell from the specs exactly what to expect from a lens with internal focus in this regard. Furthermore, it is quite conceivable that a lens that is preferable from the first point of view (reproduction ratio and working distance) may be less ideal from the second point of view (the extent to which AoV and the location of the entrance pupil changes with the focus distance) and vice versa.