## Calculating magnification of objective on telephoto lens

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### Re: Calculating magnification of objective on telephoto lens

So why should the telephoto lens if set to infinity, have any effect at all on the light exiting an infinity-corrected objective? Doesn't an infinity-corrected objective behave the same way as a lens set to infinity? I don't understand at all.

I don't understand how any of this works; can anyone explain all this about dividing focal lengths and how and why they work, in even simpler terms? I don't understand how a 5x lens when used on a 100mm lens set at infinity should give anything other than 5x in the end.

Why should focal length matter if everything is set to infinity and infinity-corrected? It makes zero sense to me, what am I missing???

Pau
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### Re: Calculating magnification of objective on telephoto lens

Don't worry.
People can drive a car perfectly without understanding how its motor works, can use a computer without a good knowledge of the microchip structure or software languages and so, and most photographers ignore many aspects of Optics and Psychics of the light.

Understanding the physical principles is very convenient but not indispensable.

Pau

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### Re: Calculating magnification of objective on telephoto lens

Pau wrote:
Thu Oct 28, 2021 10:29 am

Don't worry.
People can drive a car perfectly without understanding how its motor works, can use a computer without a good knowledge of the microchip structure or software languages and so, and most photographers ignore many aspects of Optics and Psychics of the light.

Understanding the physical principles is very convenient but not indispensable.

Thank you. I really do appreciate the advice and time others here have shared and do share. It's just that I don't understand the advice, as it has been explained to me.

I don't know what I should do, so I can get 20x MF and 10x MF with using a 200mm lens I do have, and hopefully a 100mm lens (so I can make use of its specific lens adapters I've already purchased). I don't know what I should do, and I'm very sad that all my effort and funds for over a year have been seemingly wasted, all pursued in vain for an expected magnification that is now seemingly impossible with the equipment I've worked so long and hard to finance.

Everything I thought I knew is turned upside-down; at least, not completely upside-down, because at least then I could reverse my thought process and understand the opposite. Nothing makes sense anymore.

rjlittlefield
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### Re: Calculating magnification of objective on telephoto lens

Thu Oct 28, 2021 9:56 am
I've read and re-read everything very carefully, but I cannot understand any of it. My whole setup and everything I've purchased so far seems like it's now worthless for my needs. I've wasted so much of my hard-earned money, I can't believe it; over a year's worth of savings, down the drain.
First, I advise to sit down and take several deep breaths, slowly and calmly. It is very likely that your money has been spent well and your equipment will work fine.

Then, let us start again at the beginning. Please tell us a few things:
• What camera body do you have?
• What size things do you want to photograph?
• Exactly what lenses and objectives do you have, and/or have you ordered?
I will leave your other questions untouched for the moment, because it seems that technical explanations are not helping at this time.

--Rik

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### Re: Calculating magnification of objective on telephoto lens

rjlittlefield wrote:
Thu Oct 28, 2021 10:55 am
Thu Oct 28, 2021 9:56 am
I've read and re-read everything very carefully, but I cannot understand any of it. My whole setup and everything I've purchased so far seems like it's now worthless for my needs. I've wasted so much of my hard-earned money, I can't believe it; over a year's worth of savings, down the drain.
First, I advise to sit down and take several deep breaths, slowly and calmly. It is very likely that your money has been spent well and your equipment will work fine.

Then, let us start again at the beginning. Please tell us a few things:
• What camera body do you have?
• What size things do you want to photograph?
• Exactly what lenses and objectives do you have, and/or have you ordered?
I will leave your other questions untouched for the moment, because it seems that technical explanations are not helping at this time.

--Rik
Okay, thank you.

I currently own:
-Canon EOS 500D (Rebel T1i) 15.1 megapixel DSLR

-SMC Pentax-A 645 200mm F4 (manual focus) lens; I was planning on ordering an SMC Pentax-M 100mm f/2.8 telephoto lens; Canon 60mm f/2.8 USM Macro lens; (3) female RMS to front lens and (1) M26 female thread/male RMS thread to female RMS thread front lens adapters, and lens to camera body mount adapters for all lenses

-The subjects I want to photograph are anywhere from less than 1mm to nearly 20mm in length, most being between 2-10mm; these are biological inclusions in amber, and most are situated roughly 5-15mm below the amber's surface; a long working distance is of utmost importance

-No objectives yet, was planning on saving that expense (hopefully just one) for last; anything over \$1k would take me well over a yea to finance in itself, and I only have enough saved for something under \$500 at the moment (i.e., Lightglass Optics' 5x Mitutoyo).

My makeshift copy stand is nothing more than a wood board with (4) 1.5" rubber feet on the underside, a floor flange mount, and a 1/2" threaded steel pipe 24" long; I still have to purchase (3) 160 lumen gooseneck clip-on LED lights, a Manfrotto Super Clamp, and a SWEBO LS-001 manual focus rail (it is arca-swiss compatible, mounting directly into the QR plate receptacle on my tripod's ball head). I want to finish this before I purchase an objective, mainly because I can't take proper stacked photos without the focus rail at very least.

I thought I had everything figured out.

Scarodactyl
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### Re: Calculating magnification of objective on telephoto lens

Thu Oct 28, 2021 10:23 am
So why should the telephoto lens if set to infinity, have any effect at all on the light exiting an infinity-corrected objective? Doesn't an infinity-corrected objective behave the same way as a lens set to infinity? I don't understand at all.
This one is easy enough. An infinity corrected objective actually does the opposite of what a lens focused to infinity does. The objective when used to spec grabs an image from a fixed distance in front of the lens, then sends an image focused to infinity out the back. A lens focused to infinity accepts an infinity focused image in the front and puts out an image focused to a particular distance (ie, onto the sensor) out the back. Put the two together and you get a focused image onto your camera sensor.

lothman
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### Re: Calculating magnification of objective on telephoto lens

Thu Oct 28, 2021 11:39 am
-The subjects I want to photograph are anywhere from less than 1mm to nearly 20mm in length, most being between 2-10mm; these are biological inclusions in amber, and most are situated roughly 5-15mm below the amber's surface; a long working distance is of utmost importance
this sounds perfect for the Laowa 2,5-5x lens, a lens what I own myself and it shines even on the very demanding high resolution Sony A7r4.
https://www.venuslens.net/product/laowa ... a-macro-2/

on Canon APS-C this will give you an image width from 5mm to 10mm. There is also a LED-ringlight and a tripod clamp available. I see them very often used for around 350-450\$ because some of the buyers weren't aware what effort it takes to stack images (what is often needed at such magnification).

Lou Jost
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### Re: Calculating magnification of objective on telephoto lens

I hate to add another note of complexity to this, but higher-NA objectives may have trouble imaging deep inclusions, because they usually are not designed to shoot through a thick medium. For this reason, the suggestion of a Laowa 2.5x-5x lens is a wise one, because it can be stopped down, reducing the problems of shooting through the medium if needed.

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### Re: Calculating magnification of objective on telephoto lens

Scarodactyl wrote:
Thu Oct 28, 2021 11:57 am
Thu Oct 28, 2021 10:23 am
So why should the telephoto lens if set to infinity, have any effect at all on the light exiting an infinity-corrected objective? Doesn't an infinity-corrected objective behave the same way as a lens set to infinity? I don't understand at all.
This one is easy enough. An infinity corrected objective actually does the opposite of what a lens focused to infinity does. The objective when used to spec grabs an image from a fixed distance in front of the lens, then sends an image focused to infinity out the back. A lens focused to infinity accepts an infinity focused image in the front and puts out an image focused to a particular distance (ie, onto the sensor) out the back. Put the two together and you get a focused image onto your camera sensor.
Thank you, I think I understand.

So would using just a 5x infinity-corrected objective give the same magnification when used with any lens set to infinity, regardless of its focal length? If this isn't the case, I'm not sure I understand what focal length even means or how it works. I don't know what to think; it would be nice if there were diagrams that could depict how focal length works in these situations.

I wish I had seen that Laowa lens from the very beginning; I could have saved so much money and time. I don't know if I should get the Laowa and sell all my other adapters and the 200mm lens, or stay the course and get a Mitutoyo objective (if that's even an option, to get 10x-20x MF with a 200mm or 100mm lens). I wouldn't think there's much of a market for used specialty thread adapters.

I'm just so disappointed in myself, and sick to my stomach thinking how much I spent on equipment, all under a false knowledge of how lenses work. I don't know what I'm going to do with it all.

JKT
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### Re: Calculating magnification of objective on telephoto lens

Thu Oct 28, 2021 7:37 pm
So would using just a 5x infinity-corrected objective give the same magnification when used with any lens set to infinity, regardless of its focal length?
Not so. Remember the part about added magnification with telephoto lenses. When you take a picture of far objects with lenses with different focal length, you get a different part of the landscape into the picture. The same happens here as the light coming from the microscope objective behaves the same way as the light coming from far objects or stars.

The microscope objective is designed to work with a tube lens of certain length. With such tube length the nominal magnification is achieved. Different focal lengths give you different magnifications, but there are couple of other limiting factors, which come to play when you are using different tube lengths. With shorter tube lenses and lower magnification you compress the image created by the objective to smaller area than intended. That part will be sharper, but it may be smaller than your sensor. This can happen with the nominal tube length as well. It depends on the designed image circle of the objective and your sensor size. You have to know what kind of image circle your objective delivers.

Going to a larger tube lengths you can run into so called empty magnification. You'll always get a larger image, but you might not get any additional details in it. That is because your microscope objective also has inherent resolution it can deliver. This is designed to work with the nominal tube lens and in the intended use of the objective. When you magnify the image, the limiting resolution can be that of the microscope objective instead of the sensor you are using. It is possible to calculate what is the best possible resolution of the microscope objective, but it is not possible to know what it actually delivers without testing. With quality objectives that is usually very close to the maximum, but with others you never know.
Last edited by JKT on Fri Oct 29, 2021 12:43 am, edited 1 time in total.

rjlittlefield
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### Re: Calculating magnification of objective on telephoto lens

As Lou Jost points out, it matters quite a lot that your subjects lie deep within an amber block. I say "deep" because 5-15 mm is plenty of distance to wreak havoc with image quality if the amber is at all non-uniform or has a surface that is not perfectly smooth, planar, and perpendicular to the lens axis. Under ideal conditions (perfectly uniform amber, with a surface that is smooth, planar, and perpendicular to the lens axis), a 5X NA 0.14 objective can look through 10 mm of amber with no problem. But a 10X NA 0.28 objective will be hazy, and a 20X NA 0.42 objective will be very hazy, almost unusable. Introduce any non-uniformity, or surface roughness or curvature, or a slightly off-angle view, and all the images get worse, much more so at larger magnification and NA.

So, your fundamental problem is the amber.

You have written several times of wanting/needing 10x-20x. I guess this number comes from wanting to image a 1-2 mm inclusion across the entire width of your camera's sensor. But in any case, thinking of "10X-20X" is the wrong target. Instead, you should be thinking about how you can get the best image possible of a 1-2 mm inclusion, behind 5-15 mm of amber, for whatever your budget will allow.

At this point in time, my read is that the Laowa 2.5-5X ultra macro is the best lens for that job. It is significantly cheaper than the Mitutoyo 5X, even from Lightglass Optics, and it offers the huge advantage of providing an easily adjusted aperture, which can be used to optimize image quality in the presence of imperfect amber. If you want more magnification, to put more pixels on the same optical image, then you might add a cheap teleconverter behind the Laowa. But don't do that until you see what you can get from the Laowa by itself.
I'm just so disappointed in myself, and sick to my stomach thinking how much I spent on equipment, all under a false knowledge of how lenses work. I don't know what I'm going to do with it all.
Again, the first thing to do is to take several deep breaths. From what I see so far, you probably got the 200 mm lens used, so you can resell that for essentially the same price. Nobody tracks number of owners on these things. The specialty thread adapters are worth almost as much used as new, since they don't wear out, so the major loss there is shipping. For starters, list them in Equipment Exchange here at PMN.

As for false knowledge of how lenses work, yeah, that's a problem. Maybe we can fix that with some further discussions. But when you ask "would using just a 5x infinity-corrected objective give the same magnification when used with any lens set to infinity", after I've written the explanation at viewtopic.php?p=277617#p277617 , I have to confess that I have no idea how to fix your understandings. Perhaps the explanation given by JKT, in the previous reply, will do the trick.

--Rik

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### Re: Calculating magnification of objective on telephoto lens

Thank you, JKT, Rik, and everyone here; I really appreciate your help and advice. Thank you, lothman for suggesting the Laowa lens; from seeing their site's sample images, maybe it will work for what I have in mind.

I'm sorry, but I'm still not understanding this whole concept of paired lenses and magnification, I probably never will. So it appears that the best thing I can do is just sell my lens and adapters, and get the Laowa? Maybe it would be best if I just sold my EOS 500D as well, and try to upgrade to a higher megapixel camera. Sadly, this is definitely going to delay my setup completion back several months; at least I can now allocate more spare time for lapidary work on my rough material (I don't have a cabbing machine, so I do everything by hand).

I prepare my rough material so that not even the finest of scratches remain on the surface (often spending several hours on a single, small piece), even re-finishing specimens I've purchased in preparation for photography; still, I could always immerse the specimens in cedar oil to match the refractive index and eliminate the issues of rounded surfaces and blemishes, but then I'd need some way to immerse the tip of the Laowa lens into the medium without any of it entering the lens (plastic wrap would certainly ruin image quality, and I don't know of any form-fitting glass made for this particular lens). Shortly, I'll send Laowa an email asking about this.

I'll try listing my equipment here, eventually; I'm not sure if my custom thread adapters will ever sell, but I'll try. The only other camera I have is a cheap Samsung WB35F, and its image quality isn't good, especially when trying to sell a lens. Maybe it'll work, but as usual, I don't know.

-Kaegen

JKT
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### Re: Calculating magnification of objective on telephoto lens

You don't want to use the Laowa in immersion even if you could. The optical formula is not designed for that. It is designed for air. You may get away with the amount of effective immersion in the amber, but you definitely don't want to multiply that amount.

rjlittlefield
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### Re: Calculating magnification of objective on telephoto lens

Fri Oct 29, 2021 10:16 am
Maybe it would be best if I just sold my EOS 500D as well
For whatever it's worth, I still use my EOS 500D more often than any other camera. Surely it's not the best sensor available, but it works very nicely for what I do and it tethers much better than my Nikon D800e. So, my recommendation is to use the 500D until you have everything else working so well that the camera becomes a limiting factor.
immerse the specimens in cedar oil..., but then I'd need some way to immerse the tip of the Laowa lens into the medium without any of it entering the lens
I suggest instead, use a vertical setup so that your subject surface is horizontal, then use cedar oil plus a glass cover slip sitting on top of it. The glass cover slip provides the planar surface that you need, and the lens works in air as it was designed to do.

I'm still not understanding this whole concept of paired lenses and magnification
Maybe some ray traces will help.

Here are a couple of grossly simplified schematic diagrams of a 5X infinity objective, paired with a 200 mm tube lens so as to give actual 5X magnification. The objective is focal length 40 mm, 5 = 200/40.

First, here are the light rays for a single point in the middle of the frame. You can see that the objective accepts diverging rays from the subject, redirects them to be parallel ("focused at infinity") in the space between lenses, then the tube lens takes those parallel rays and focuses them down to a point in the image plane. You can't see anything about magnification in this first diagram; it's just to show how the lenses redirect the light from a single point on the subject to a single point on the image.

Now, I have removed the labels, but added an off-center point on the subject. Again, the objective accepts diverging rays from the subject and redirects them so as to be parallel with each other. In the infinity space, the rays from the off-center point are not parallel to the optical axis -- that's what keeps them distinct from the rays for the center point. Then the tube lens takes those parallel rays for the off-center point, and refocuses them back to a point in the image plane.

In this second image you can see where the magnification comes from. The objective is 40 mm from the subject, but the tube lens is 200 mm from the image. That 5:1 ratio of distances means the light can spread out 5 times farther behind the tube lens, than it was in front of the objective. Corresponding points are 200/40 = 5 times farther apart in the image plane, than they are in the subject plane. The magnification is always just the ratio of focal lengths of the objective and tube lens -- as long as everything is set up so that the tube lens is "focused at infinity" so you get those bundles of parallel light rays between the objective and tube lens.

In actual practice there are lots of lens elements and the ray traces get very complicated inside the objective and tube lens. But outside the lenses, the ray traces still look just like these diagrams. So in practice, you get to ignore the complexity because that happens inside the lenses where you can't see it anyway.

Does this help?

--Rik

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### Re: Calculating magnification of objective on telephoto lens

Thank you so much for your time and effort in preparing those diagrams, Rik! The first one does make some sense to me, but I don't think I'll ever grasp the concept; just for an example, as I'm not the most capable (I failed all my tests in high school Physics), to this day I cannot understand even how to make a simple electrical circuit, much less understanding how transistors work. Sadly, anything physics-related is incomprehensible to me; I thought I knew what I was doing, but it seems it was all wrong.

Yes, my setup will be a y-axis or vertical setup, utilizing a basic copy stand design. The main thing I've been worried about with this setup, is the fact that the 3/8-16 thread stud of the Manfrotto Super Clamp is made of brass; I've looked and asked everywhere about the "shear force" limits of the stud, but haven't gotten any answers. I'm concerned that the weight of the attached components will be too great.

Most of my amber specimens are not perfectly flat, and many of them are sizeable (100+ grams) with multiple rare inclusions (centipedes, Ophiocordyceps fungus-infected ants, etc.) within the same piece, and some really belong in museums; I wouldn't want to cut up such specimens, as it would destroy their value, so maybe sticking with air as a medium is the best route. However, that is an excellent idea using a cover glass on top of the amber, and I think I have a few small, common specimens I can do that with. I would not mind trying that out!

I think I'll give up on trying to purchase an objective for a paired lens setup; also, since you recommend it, I'll hold onto the EOS 500D and see how it works with the Laowa 25mm f/2.8 lens. That was also an excellent suggestion, I think I may need to eventually get a teleconverter; I do see a FotodioX 2x Canon EF converter for about \$100 on B&H's website, and I'll have to look at more reviews to see if it generally performs well.

I guess the trick will be to see if I can manage to sell my adapters and lens.

Thank you so much! I think I'm starting to accept the situation, and maybe things will turn out all right.