# Focal length vs magnification



## TreeofLifeStairs (Feb 16, 2014)

Is there a correlation between focal length and magnification? I've seen lenses that say that they are 1:1 or 1:4 or so on but the focal lengths don't seem to be consistent. Am I not understanding how magnification works? I feel I have a pretty good grasp on how focal length effects a picture.


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## 480sparky (Feb 16, 2014)

Magnification is the ratio between the subject's real size compared to it's projected size on the film/sensor.

A 10mm object that appears 5mm across on the film/sensor will have a 1:2 magnification ratio.  If it is projected at 20mm on the film/sensor, it will have a 2:1 mag ratio.


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## TreeofLifeStairs (Feb 16, 2014)

So for example if I have lens that is a 50mm 1:1 and one that is 200mm 1:1 then the subject would be the same size in the frame but allows the camera to be farther away from the subject? The focal length would just change the perspective then or no?


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## 480sparky (Feb 16, 2014)

TreeofLifeStairs said:


> So for example if I have lens that is a 50mm 1:1 and one that is 200mm 1:1 then the subject would be the same size in the frame but allows the camera to be farther away from the subject? The focal length would just change the perspective then or no?



Not _just_ the perspective.  The DOF would change accordingly.


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## KmH (Feb 16, 2014)

Understanding Camera Lenses


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## Gavjenks (Feb 16, 2014)

> Is there a correlation between focal length and magnification?


A CORRELATION? No, not at all.

A RELATIONSHIP? Yes. Obtaining a given magnification _with a particular perspective_ (distance from the subject) is only possible with a single focal length. However, obtaining a given magnification simply by itself, with no other stipulations, is possible with any focal length, thus zero correlation between specifically those two variables alone.



For example, 50mm lens (with no extension tube) at a distance of 1 meter will have precisely the same magnification as a 100mm lens at a distance of 2 meters.
So you can get the same magnification with either focal length. But the images won't be identical. The stuff nearest the lens will be exaggerated in size in the 50mm as compared to the 100mm (such as a person's nose compared to their ears), due to geometric perspective.

Distance often matters. In the above example, it can matter by making people's proportions look closer to how we are more used to seeing them (further than a meter away for sure!) When taking photos of bugs or birds, distance for the same magnification is helpful to not scare them off, etc.


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## JerryLove (Feb 16, 2014)

I'm guessing: but I suspect that the magnification (1:1, or 1:4, for example) is a function of focal length and minimum focus distance combined. The longer the focal length, the bigger the item as projected on the sensor. The closer you physically are: the larger the item as projected on the sensor. 

What macro lenses have isn't so much high focal lengths (some do), but rather very short minimum focus distances.


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## Gavjenks (Feb 16, 2014)

> magnification (1:1, or 1:4, for example) is a function of focal length and minimum focus distance combined.


The MAXIMUM (in focus) magnification of the lens, yes. The actual magnification for a given shot changes depending on how far you are focusing at the moment.

For example, let's say a lens has a maximum magnification of 1:2 @50mm. That doesn't mean that whenever you're at 50mm you have 1:2 magnification. Only if you are currently for this particular shot aiming at something right at your minimum focal distance.

If you don't change any settings, but focus on something further away, you have a lower magnification.


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## Overread (Feb 16, 2014)

480sparky said:


> TreeofLifeStairs said:
> 
> 
> > So for example if I have lens that is a 50mm 1:1 and one that is 200mm 1:1 then the subject would be the same size in the frame but allows the camera to be farther away from the subject? The focal length would just change the perspective then or no?
> ...



As far as I've ever worked out the depth of field remains identical. 

A 50mm and a 200mm lens at the same magnification of 1:1 will give you the same frame content and the same depth of field. What will change is

1)The distance from the subject - the longer the focal length the further away (which tends to correspond to a greater working distance)

2) The degree of background blurring. The longer the focal length the quicker the fall off into blur and the greater the degree of blurring. This gives the impression that shorter focal lengths give more depth of field because the drop off into blur is less noticeable then it is with a longer focal length macro lens. 


Minimum focusing distance - distance from the sensor/film to the subject
Working distance - distance from the front of the lens to the subject. (typically only important and referenced in macro photography).


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## Gavjenks (Feb 16, 2014)

> As far as I've ever worked out the depth of field remains identical.


It's complicated. It is close to identical at higher magnifications. At lower ones, there are huge differences:
http://theonlinephotographer.typepad.com/.a/6a00df351e888f883401157149a571970b-800wi

Not to mention that DOF changes with aperture for example, while magnification does not.


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## Overread (Feb 16, 2014)

Aye for the human eye and in real world context its basically impossible to tell - the biggest visual difference you might get is if one lens happens to internally operate differently. Most macro lenses on the modern market reduce their focal length and aperture as they focus closer to 1:1. However from what I gather most land around a similar rough aperture value - I don't think there are any extreme options that land far wider or smaller than the others to really give a big difference.


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## WayneF (Feb 16, 2014)

Gavjenks said:


> > Is there a correlation between focal length and magnification?
> 
> 
> A CORRELATION? No, not at all.
> ...




There are a couple of ways to look at it, but you confused them.   You referred to subject size, but  you just showed that a 100mm lens has 2x the magnification of a 50mm  lens.

Focal length is exactly magnification.  That is the only reason we use telephoto, to magnify the subject size.
4x focal length will be a view 1/4 as wide, but the subject image size will be 4x larger.  That is magnification.

However, macro distance does not compare two  magnifications of image size, but instead compares image size to size on  the sensor (reproduction ratio). 
(Almost) any macro lens can do 1:1 reproduction, regardless of focal length.  That is a matter of focusing closer.


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## KmH (Feb 16, 2014)

Overread said:


> 2) The degree of background blurring. The longer the focal length the quicker the fall off into blur and the greater the degree of blurring.


The degree of background blurring also stays the same.
The longer focal length magnifies the blurred background elements (background compression) but does not blur the background more.
The longer focal length also has a narrower field-of-view so less of the blurred background is in the image frame.


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## Derrel (Feb 16, 2014)

Gavjenks said:


> > As far as I've ever worked out the depth of field remains identical.
> 
> 
> It's complicated. It is close to identical at higher magnifications.



A number of years back, I shot 1:1 magnification images using my 60mm Micro-Nikkor and my Sigma 180 f/3.5 EX Macro...I got what appeared to me to be the same depth of field with the 180mm lens as I did with the 60mm, despite the 180mm lens being 3x farther away...it kind of made an impression on me...


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## 480sparky (Feb 16, 2014)

WayneF said:


> Gavjenks said:
> 
> 
> > > Is there a correlation between focal length and magnification?
> ...



Not when you double the distance between the camera & subject.


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## WayneF (Feb 16, 2014)

480sparky said:


> Not when you double the distance between the camera & subject.



?   Doubling the distance makes the subject size smaller.  Keeping it same size with longer focal length is exactly magnification.  Really, you know these things.


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## 480sparky (Feb 16, 2014)

WayneF said:


> 480sparky said:
> 
> 
> > Not when you double the distance between the camera & subject.
> ...



Try reading the post again.



Gavjenks said:


> ......For example, 50mm lens (with no extension tube) at a distance of 1 meter  will have precisely the same magnification as a 100mm lens at a  distance of 2 meters........


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## WayneF (Feb 16, 2014)

480sparky said:


> WayneF said:
> 
> 
> > 480sparky said:
> ...




?  Because he said it wrong does not make it meaningful.  

The 50mm had the same IMAGE SIZE, only   **BECAUSE** the 100mm at 2x distance also has 2x the magnification.   

At the same distance, the 100mm would see 2x image size (magnification), because 2x focal length has 2x magnification.


Read Magnification - Wikipedia, the free encyclopedia


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## 480sparky (Feb 16, 2014)

WayneF said:


> ?  Because he said it wrong does not make it meaningful.
> 
> The 50mm had the same IMAGE SIZE, only   **BECAUSE** the 100mm at 2x distance also has 2x the magnification.
> 
> ...



Once again...... read the post.



Gavjenks said:


> ......For example, 50mm lens (with no extension  tube) _*at a distance of 1 meter*_ will have precisely the same  magnification as a 100mm lens _*at a  distance of 2  meters.*_.......






If you can't figure this out, I'm not going to try to correct you any more.


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## Gavjenks (Feb 16, 2014)

> Focal length is exactly magnification. That is the only reason we use telephoto, to magnify the subject size.


This is simply incorrect. It's not magnification, and that's not the only (or even a very common) reason to use telephoto.
You primarily use telephoto not to magnify, but rather *to get further away from the subject*. Or conversely, to take photos of things you can't get close to.

If a human being is the subject of your photo takes up exactly one half the height of your frame in focus, then your magnification is the same, no matter which focal length you take that photo with.  Longer focal lengths are useful though, because if you take it with 15mm lens, you have the same magnification, but the person will look weird since you're closer than you normally are to people. With 100mm lens, same magnification, it looks more normal, because you're 10-15 feet away.

Distance away from a subject =/= magnification.
Magnification = how big a thing is on your sensor compared to how big it is in real life.

If you are 15 miles away from a ladybug, and take a photo of it that fills half of your frame using a lens the size of an apartment building, then your lens still has *LESS magnification* than if you are a foot away from the ladybug and take a photo where it fills the entire frame.

The problem here is just that you're using a colloquial definition of magnification where it is actually a pretty specific technical term in photography (and biology, etc. etc. same technical definition) where focal length is just one of two variables you need to solve the equation.





> A number of years back, I shot 1:1 magnification images using my 60mm Micro-Nikkor and my Sigma 180 f/3.5 EX Macro...I got what appeared to me to be the same depth of field with the 180mm lens as I did with the 60mm, despite the 180mm lens being 3x farther away...it kind of made an impression on me...


Well yeah, the chart above seems to show that it becomes essentially indistinguishable as low as 0.05 magnification. So if you're shooting 1:1, the DOF will long past being affected, probably completely indistinguishable / sub-pixel differences kind of thing.

At 0.01 magnification and lower, though, it's a major difference. 0.01 = things about 70 inches tall filling the vertical on a full frame camera.  In other words, something along the lines of a seated human portrait with plenty of space above the head.


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## WayneF (Feb 17, 2014)

Gavjenks said:


> > Focal length is exactly magnification. That is the only reason we use telephoto, to magnify the subject size.
> 
> 
> This is simply incorrect. It's not magnification, and that's not the only (or even a very common) reason to use telephoto.
> You primarily use telephoto not to magnify, but rather *to get further away from the subject*. Or conversely, to take photos of things you can't get close to.




? Sorry, you are choosing your terms carelessly, not well at all.  You are assigning new meanings of your own, and then imagining it must be fact.  

You are using magnification to instead mean image size.  Magnification is the math RATIO of ORIGINAL subject size to sensor image size.

The absolute fact is that if a 50mm and 100mm lens are at the SAME distance, the 50mm image size is HALF of the 100mm image size (obviously because 100mm magnifies 2x compared to 50mm).  That is what focal length does.  That is all it does.

The telephoto lens ONLY works because of its greater magnification, THAT is why we use it.  The ONLY reason we can stand farther away is because the focal length magnifies to produce the same usable image size.  How hard is that? 



> If you are 15 miles away from a ladybug, and take a photo of it that fills half of your frame using a lens the size of an apartment building, then your lens still has *LESS magnification* than if you are a foot away from the ladybug and take a photo where it fills the entire frame.



Your lady bug terms forget everything except image size.   We can get image size different ways, long lens magnification, closeup subject distance, cropped sensor size, etc.   It was the one foot distance that produced your larger image, it was not about lens magnification.   It possibly could have been the same lens, with proper extension.

However, then macro does shift the definitions, and 1:1 is about reproduction ratio (compared only to sensor size), and it is not called lens magnification (it was instead about subject distance).    Any focal length can produce 1:1 (with proper extension).


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## Gavjenks (Feb 17, 2014)

*Facepalm* Dude you just contradicted your own definition within a single post.



> Magnification is the math RATIO of ORIGINAL subject size to sensor image size.


^
Your words. Which are correct.
A ladybug is a given physical size. The ladybug's size doesn't change when you switch lenses.  And if you fill up your frame equally with a ladybug with two lenses, then the image size is ALSO the same.



So guess what? The ratio of the original subject size to the image size on the sensor is the SAME! X/Y = X/Y...
Thus the magnification is the same when you make an equally framed image of the same object.
A 50mm lens at 1 foot will make the ladybug the same size on the sensor as a 100mm lens at 2 feet.

Therefore, by your definition, since neither subject size nor image size are changing, the 50mm and the 100mm lens *CAN *have the same magnification. Therefore *focal length =/= magnification.
100mm at 2 feet:* ladybug = quarter inch real life, let's say 1/16 inch on the sensor = *1:4 magnification*
*50mm at 1 foot:*  ladybug = quarter inch real life, let's say 1/16 inch on the sensor = *1:4 magnification*

They CAN also not have the same magnification, under different circumstances, like the situation you are describing where they are at the same distance. But when you say things like "focal length = magnification" you are wrong, because that implies always. When in fact, it is only true in the _specific and narrow _situation of not changing your distance to the subject. It is false in every. other. instance. (infinitely more situations)



> However, then macro does shift the definitions


Um, no. It doesn't. It's still the exact same definition. Ratio of object size to image size. It's called "Macro" when the ratio = 1. Simple as that. Just an arbitrary cutoff point somebody decided on. The fact that any focal length can provide 1:1 is in fact an example of why focal length does NOT = magnification. You provided your own counterexample to yourself. Thanks.


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## WayneF (Feb 17, 2014)

Gavjenks said:


> ......For example, 50mm lens (with no extension tube) at a distance of 1  meter  will have precisely the same magnification as a 100mm lens at a   distance of 2 meters........



My objection was about the above careless statement.  Confusing misuse of terms.  It does not point newbies in the right direction.

The principle is this:

If both 50mm and 100mm lenses are at the SAME distance, the 50mm image is of course smaller, because 100mm is 2x relative magnification, due to focal length.

The magnification of the longer lens (2x focal length) allows us to stand back 2x as far, and still get the same image size, instead of half size.

That result is NOT the same magnification.  It is merely the same image size, specifically due to different magnification.

We can change IMAGE SIZE with focal length magnification, or with closer subject distance, or by cropping sensor size.


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## Gavjenks (Feb 17, 2014)

There is absolutely nothing misleading or incorrect about my 50 / 100 statement. 

There is, however, something incorrect about this statement:


> The magnification of the longer lens (2x focal length) allows us to stand back 2x as far, and still get the same image size, instead of half size.


NO. No no no no. The magnification_* IS NOT 2x*_ for the longer lens in that situation.

The magnification is precisely the same. I don't comprehend how you can continue to give the proper definition, and yet fail to even attempt to apply it.
Again, I will quote your own very words, which were correct, about the definition of magnification:


> _Magnification is the math RATIO of ORIGINAL subject size to sensor image size._



Do the math!
Magnification = sensor size / actual size
In the situation I described, the actual size is the same, obviously, since lens choice doesn't make objects bigger or smaller. Let's say it is X in both cases.
In the situation I described, the sensor size is ALSO the same since the object fills the same portion of the frame. Let's say it is Y in both cases.
*Magnification = sensor size / actual size = Y/X.  Y/X = Y/X    Therefore, both lenses have the same magnification.*



What you're doing is *exactly *like saying "Density = Mass / Volume" and then a paragraph later saying "A big piece of wood is denser than a small piece of wood, because the mass is larger"


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## Ysarex (Feb 17, 2014)

WayneF said:


> Gavjenks said:
> 
> 
> > ......For example, 50mm lens (with no extension tube) at a distance of 1  meter  will have precisely the same magnification as a 100mm lens at a   distance of 2 meters........
> ...



You are confused. Go back to the OP's original question where he asked about magnification and gave examples using the common photo form 1:1 or 1:4. The OP's question establishes the context and Gavs was precisely correct to answer the OP saying there is no correlation between FL and magnification. Look up the definition of correlation (nobody here would understand that better than Gavs). As Gavs pointed out you yourself verified the definition correctly: "Magnification is the math RATIO of ORIGINAL subject size to sensor image size."

In any two photos with the same image size of the subject recorded (regardless of the cropped size of the sensor -- you're wrong about that also) the magnification is the same.

In a photo where the magnification is 1:4, which of those two numerals is the lens focal length? The 1 or the 4?

Joe


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## Derrel (Feb 17, 2014)

Luckily, I bought my ticket outside the arena from a guy who was having trouble unloading a set of three tickets and one single nose-bleed section seat...and I payed LESS than half of face value! Now, the fellow was asking TWICE (that's 2x!!!) face value, and I told him I'd give him HALF price...he blurted out "SOLD!" immediately.


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## Gavjenks (Feb 17, 2014)

> which of those two numerals is the lens focal length? The 1 or the 4?



(creative commons)


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## WayneF (Feb 17, 2014)

Gavjenks said:


> NO. No no no no. The magnification_* IS NOT 2x*_ for the longer lens in that situation.



Present company excepted, but anyone that does not realize long lenses magnify the subject (much like telescopes), has passed hopelessness.



> Do the math!
> Magnification = sensor size / actual size



Sensor size?   So you did not mean magnification, you instead meant reproduction ratio?     (except that is not about sensor size either).

Magnification is about Original subject size compared to the image size on the sensor.  Not to the sensor size, but magnification compares image size.   And a 100mm lens obviously magnifies 2x compared to a 50 mm.  You have looked through different lenses on a SLR, right?

Read here:  Magnification - Wikipedia, the free encyclopedia


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## Gavjenks (Feb 17, 2014)

"Sensor size" was shorthand for "size of the image on the sensor."  I was not perfectly careful with my word choice since you already explained it yourself... Sorry, whatever.
The fact remains that in both situations, neither the size of the image on the sensor, nor the size of the object are changing, thus the magnification cannot change.

You continuing to just say "lol nope!" without addressing the math or the logic is not exactly convincing.




> Read here: Magnification - Wikipedia, the free encyclopedia


Don't mind if I do!  According the wikipedia:




f = focal length
do = distance lens to object

In other words, focal length is NOT equal to magnification. That would be "M = f" or "M = constant * f" neither of which as you can see, is the equation.
If you plug in my examples, you'll see once again that 50mm and 100mm lenses can both indeed have *equal* magnification:

50mm @1 foot (~300mm):
M = 50 / (50 - 300) = 1:5 magnification   (the negative sign just means the image is flipped like in any focused camera)

100mm @2 feet (~600mm):
M  100 / (100-600) = 1:5 magnification.



Oh hey look the magnification is the *same. 
*As in... not 2x higher in the 100mm lens. Imagine that.

Yes, it's possible to describe a situation where the 100mm has twice the magnification (when you stand in the same place). _It's also equally possible to describe a situation where the 50mm has twice the magnification_ (if you stand 4x closer), or anything in between or whatever else you want. Saying that "100mm lenses have 2x the magnification, period" means "in every situation" which is not true. It is in fact only one situation, an infinitely small percentage. And no correlation.


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## WayneF (Feb 17, 2014)

Gavjenks said:


> I was not perfectly careful with my word choice



Yes, that has been my complaint.




> f = focal length
> do = distance lens to object



There are factors of magnification... focal length is certainly one, and subject distance.

But to  examine only the effect of the focal length  -- If  we compute for 50mm at 2 feet, and 100m at the same 2 feet,
clearly as everyone knows, long lenses obviously magnify the result we see (2x in that comparison).



> As in... not 2x higher in the 100mm lens. Imagine that.



My objection is to your saying "no it doesn't", which is clearly nonsense.


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## Gavjenks (Feb 17, 2014)

> There are factors of magnification... focal length is certainly one, and subject distance.



Yep. Which is why:


> long lenses magnify the subject





> And a 100mm lens obviously magnifies 2x compared to a 50 mm.





> _The magnification of the longer lens (2x focal length)_


Are all wrong statements, since they all ignore of the two *necessary *variables. You cannot say anything meaningful about magnification while only referencing focal length and leaving distance ambiguous. Magnification is only defined at each specific distance at given focal lengths.

It is exactly as wrong, and wrong for the same reason, as the following statements would be:


> Heavy rocks are more dense.





> A 100 kilogram rock is obviously twice as dense as a 50 kilogram rock.





> _The density of the heavier rock (2x mass)_




Sure, you can imagine a possible situation where a 100kg rock *happens *to be twice as dense as a 50kg rock. But so what? You can also describe a situation where they are the same, or where the 50kg rock is denser, or anything else. So making any specific claim about their relationship based on mass alone is nonsensical.


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## WayneF (Feb 17, 2014)

Gavjenks said:


> Are all wrong statements, since they all ignore of the two *necessary *variables. You cannot say anything meaningful about magnification while only referencing focal length and leaving distance ambiguous. Magnification is only defined at each specific distance at given focal lengths.



If I stand in the same place, and switch my lens (to get a magnified view of the subject), distance is obviously NOT a variable.  A factor yes, but not a variable in this case (more terms).   Not much I can do about distance except to move.

But in use, I switched the lens specifically because it changes the magnification of the scene I see, which was the only purpose (often the purpose is view width, which is also magnification).
The formula clearly computes 2x magnification from a 2x longer focal length at the same distance.  Focal length is an extreme factor of magnification.  It is the reason why we have different focal lengths.

I suspect you know this obvious stuff, surely still just trying to defend the first wrong crap.  I'm past bored, and am abandoning this. I don't care what you think, but it seems a sin to publicly spread wrong stuff to newbies.


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## Gavjenks (Feb 17, 2014)

> *If I stand in the same place*, and switch my lens (to get a magnified view of the subject), distance is obviously NOT a variable.


You assigned a value to a variable and then said it's not a variable in the same sentence. If it truly wasn't a variable, then you wouldn't have to say anything about it at all. But you do. Because it is.



> The formula clearly computes 2x magnification from a 2x longer focal length *at the same distance.*


Yes.

"A 100mm lens gives 2x magnification _at the same distance_" is true.
However, repeatedly in this thread, you have said things like
"A 100mm lens obviously gives 2x magnification over a 50mm lens" _without _specifying anything about distance.

The first claim is true. The second claim is false. You don't seem to acknowledge the distinction, is the problem.




*It's like saying a broken watch "works" just because it happens to be right twice a day... *Why would you only focus on that one special case?


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## 480sparky (Feb 17, 2014)




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## JerryLove (Feb 17, 2014)

Perhaps answering a question will help? 

Does a telescope magnify the image of, say, the moon? Because it is less than moon-sized on my eye (or camera when I attach one), though far bigger than I see it without the telescope?


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## Gavjenks (Feb 17, 2014)

JerryLove said:


> Perhaps answering a question will help?
> 
> Does a telescope magnify the image of, say, the moon? Because it is less than moon-sized on my eye (or camera when I attach one), though far bigger than I see it without the telescope?


"Magnify" as a verb implies a comparison, which means you need to specify a baseline, which needs both a FL and a distance. If you are comparing a telescope on Earth to your eyeball on Earth, as you seem to be asking, then yes, the telescope will have a higher magnification.

However, if you were Neil Armstrong in July 1969, for instance, then your eyeball would achieve a *much *higher magnification of the moon than your telescope does from Earth. Many orders of magnitude higher magnification.

That's why it's generally confusing and unnecessary and not very useful to talk about magnifying as a verb. 




Notice that the only cameras that advertise "__x magnification!" are the crappy cheapest of the consumer point and shoots. As soon as they market to any segment of the population that might know what they're talking about, they stop talking about __x magnification, and if anything, advertise maximum system magnification as a proper ratio, not in comparison to anything (like for macro), because there's no room for ambiguity and it is better standardized and scientific.


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## TreeofLifeStairs (Feb 17, 2014)

Even though this has been a heated conversation, the back and forth has actually really helped with my understanding of the subject. Thank you to both of you.


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## petrochemist (Mar 10, 2014)

JerryLove said:


> Perhaps answering a question will help?
> 
> Does a telescope magnify the image of, say, the moon? Because it is less than moon-sized on my eye (or camera when I attach one), though far bigger than I see it without the telescope?



Your question actually contains a key part often missed out, which may be the cause of much of this confusion.
This is 'magnify THE IMAGE'
The magnification of telescopes is magnification of the image not the item itself, whilst in macro magnification refers to the items dimensions.

Gavjenks' original reply is probably the clearest explanation I've seen of magnification but still it took the best part of 2 pages of discussion to follow it up!


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