# Focal length confusion



## GaryPolter (Sep 2, 2010)

I'm a little confused by what is meant by focal length.  Wikipedia says it's both how strong the light converges and the distance from the lens to the image plane.  They also give an example that is not quite clear to me:

Assume the camera is set to a focal length of 50mm, and now I want to focus on an object 1000mm away.  Wikipedia says "the lens must be moved 2.6mm further away from the image plane".  Does this mean I change my focal length to 52.6?  

The thin lens equation says  1/u + 1/v = 1/f.  u is the distance from the lens to the object.  v is the distance from the lens to where the image is formed.  f is the focal length.  So does the image sensor go on v or f?


Focal length - Wikipedia, the free encyclopedia


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## Big Mike (Sep 2, 2010)

I'm no lens engineer, but you need to consider the 'focal point' of the lens.  Which is the point where the light converges.  This may change as the lens is focused, zoomed etc.  
So it's not the whole lens that has to physically move, just certain elements, that will adjust the focal point (or not).  :scratch:


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## GaryPolter (Sep 2, 2010)

So I did a bit more digging and came across a post on this forum (Difference between focal length and focussing distance??? - The Photo Forum - Photography Discussion Forum)*.*  In this post, one person says focal length is fixed for a lens, and you change the focal ring to move the lens closer and further to the image sensor.

Say I buy a lens with a focal length between 80mm and 210mm.  What does changing the focal length do compared to changing the focal ring (zoom)?


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## Polyphony (Sep 2, 2010)

Focal length is the distance from a lens to the point at which light going through it converges.

Doesn't get much simpler than this: http://images.trustedreviews.com/images/article/inline/3973-FocalLength_diag.gif


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## Big Mike (Sep 2, 2010)

In practical terms, I think you may be way over-thinking this.  

This isn't the type of thing you need to be thinking about when considering which lens to buy.  This is the stuff you think about when you are really bored and need to satisfy a geeky curiosity.


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## Polyphony (Sep 2, 2010)

Big Mike said:


> In practical terms, I think you may be way over-thinking this.
> 
> This isn't the type of thing you need to be thinking about when considering which lens to buy.  This is the stuff you think about when you are really bored and need to satisfy a geeky curiosity.


Or took years and years of physics classes.


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## GaryPolter (Sep 2, 2010)

Polyphony said:


> Focal length is the distance from a lens to the point at which light going through it converges.
> 
> Doesn't get much simpler than this: http://images.trustedreviews.com/images/article/inline/3973-FocalLength_diag.gif



Say I have a lens set to a focal length of 110mm.  Effectively, this means that the lens is 110mm away from the image sensor, right?

Now say I have an object 300mm away that I want to focus on.  Using the lens equation, I know that the distance from the lens to the object image plane is 173.68mm.  

How would I focus on this object?  If I adjust the focal length, then the object image plane will change...

My overall goal is to understand this diagram: http://http.developer.nvidia.com/GPUGems/elementLinks/fig23-02.jpg


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## AdrianC (Sep 2, 2010)

I don't know much about lenses, but I think you're confusing things.

The focal length tells you how much the lens zooms, basically. Then you have the focus ring which allows you to focus on whatever you want. There are two rings.


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## prodigy2k7 (Sep 2, 2010)

GaryPolter said:


> I'm a little confused by what is meant by focal length.  Wikipedia says it's both how strong the light converges and the distance from the lens to the image plane.  They also give an example that is not quite clear to me:
> 
> Assume the camera is set to a focal length of 50mm, and now I want to focus on an object 1000mm away.  Wikipedia says *"the lens must be moved 2.6mm further away from the image plane".*  Does this mean I change my focal length to 52.6?
> 
> ...



The beginning of that quote says *"To focus a distant object"* Its referring to the focusing, not the focal length. Focusing is just a small movement of lense(s) to ...focus

Im no expert but that sounds right doesn't it? i hope so ha


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## prodigy2k7 (Sep 2, 2010)

Polyphony said:


> Focal length is the distance from a lens to the point at which light going through it converges.
> 
> Doesn't get much simpler than this: http://images.trustedreviews.com/images/article/inline/3973-FocalLength_diag.gif


Ya thats what I thought, but how do you explain the EF 24-70 F/2.8L USM?

"Of note is that the 24-70mm L reverse extends - it becomes longest at 24mm as shown above. Most lenses including the 24-105 L become fully extended at their longest focal length setting."

Canon EF 24-70mm f/2.8 L USM Lens Review


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## clanthar (Sep 2, 2010)

Polyphony said:


> Focal length is the distance from a lens to the point at which light going through it converges.
> 
> Doesn't get much simpler than this: http://images.trustedreviews.com/images/article/inline/3973-FocalLength_diag.gif




This is absolutely correct. I think what you're missing is this additional information:

Lenses have a specific "focal length at infinity" where they are as close to the film/sensor as possible. A lens closer to the sensor than it's focal length at infinity isn't in focus on anything. As you focus a lens on subjects increasing closer to the sensor the focal length increases. At the point where the lens focal length is double it's infinity focal length it will be equal distant between the sensor and the subject and you'll be into the macro range of photography.

Joe


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## clanthar (Sep 2, 2010)

[/quote]
Ya thats what I thought, but how do you explain the EF 24-70 F/2.8L USM?
[/quote]

Focal length as the distance from the center of the lens (nodal point) to the film is the basic principle for simple lens designs. That all changed when this happened: P. Angenieux 35mm f/2.5. Lens designers discovered how to move the nodal point behind and/or in front of the lens center.

Joe


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## Helen B (Sep 2, 2010)

GaryPolter said:


> Assume the camera is set to a focal length of 50mm, and now I want to focus on an object 1000mm away.  Wikipedia says "the lens must be moved 2.6mm further away from the image plane".  Does this mean I change my focal length to 52.6?



No. The focal length does not change as you focus (move) the lens (except for some special lenses that shorten in focal length when focusing on close objects). In the above case the focal length stays at 50 mm. The image distance changes from 50 mm (when the lens is focused on infinity) to 52.6 mm.



> The thin lens equation says  1/u + 1/v = 1/f.  u is the distance from the lens to the object.  v is the distance from the lens to where the image is formed.  f is the focal length.  So does the image sensor go on v or f?



The sensor should be v from the thin lens. Notice that when u = infinity, f = v.

Best,
Helen


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## clanthar (Sep 2, 2010)

Yes. The focal length does change as you focus the lens on subjects increasing closer to the camera. The lenses "focal length at infinity" does not change but it's effective focal length does. If it didn't change it wouldn't be necessary to calculate a bellows compensation factor for exposure in macro photography.

I used to have a very nice Nikkor 55mm f3/5 micro lens in which you could watch the aperture change size as the focus ring was turned -- they built the bellows factor adjustment in mechanically to compensate for the increased lens focal length.

Joe


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## Helen B (Sep 2, 2010)

What you call the 'effective focal length' is usually called the image distance. The focal length does not change as you focus (no matter how close), unless the lens elements are designed to move with respect to one another to alter the focal length as the lens is focused.

The _effective aperture_ is calculated from the entrance pupil diameter and the image distance in macro work, or more properly, from the true aperture multiplied by (1+m/mp) where m is the image magnification and mp is the pupil magnification.

Best,
Helen


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## Derrel (Sep 2, 2010)

Quite a LOT of lenses lose effective focal length as they are focused closer...many,many,many lenses lose effective FL in fact...not sure where the idea that loss of focal length is "rare" or "uncommon" is coming from...


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## GaryPolter (Sep 2, 2010)

clanthar said:


> Yes. The focal length does change as you focus the lens on subjects increasing closer to the camera.





Helen B said:


> No. The focal length does not change as you focus (move) the lens  (except for some special lenses that shorten in focal length when  focusing on close objects)



Thanks to everyone for the great discussion on this topic.

I'm confused as to whether the focal length changes as you focus the camera.

If have a lens with 110mm focal length, and one object 300mm away and another 150mm away how will I know which one is in focus?  How do I control the focus without changing the focal length?


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## Derrel (Sep 2, 2010)

Yes, typically in the extreme close-up range there WILL be a loss of effective focal length with many,many lenses. Your last question, about two objects, one 300mm away and another 150mm away...you're asking how you will know which one will be in focus????

What do you mean? Only ONE object will be in focus...you can focus by moving the camera closer or farther away, or by using the focusing ring on the lens...you will not be able to bridge a distance of 150mm/300mm with depth of field to cover with a "fixed" camera...you should be able to see through the viewfinder with an SLR Camera what is in focus...


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## Helen B (Sep 2, 2010)

GaryPolter said:


> I'm confused as to whether the focal length changes as you focus the camera.



For a simple lens for which all parts (elements) of the lens move together, the focal length never changes. There are some lenses, becoming increasingly common, which deliberately shorten in focal length as they focus closer by rearranging the lens elements in a slightly similar way to what happens inside a zoom lens when it is zoomed. This allows them to have a greater focus range (magnification) without having an excessively long focus travel; better corrections at close distances; and less loss of effective aperture as they focus close. I called such lenses 'special' to try to avoid confusion with the fundamental optical principles under discussion here.



> If have a lens with 110mm focal length, and one object 300mm away and another 150mm away how will I know which one is in focus?  How do I control the focus without changing the focal length?


You move the lens in and out - ie you change the image distance. This is all the focusing helicoid does on a normal lens with no floating elements or groups.

Best,
Helen


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## Derrel (Sep 2, 2010)

You can feel free to wade through these discussions.

Actual effective focal length of 80-400 VR when close focused? - Photo.net Nikon Forum

Actual effective focal length of 80-400 VR when close focused? - Photo.net Nikon Forum

Actual effective focal length of 80-400 VR when close focused? - Photo.net Nikon Forum

Light loss in focussing closer and effective focal length/aperture - Photo.net Nikon Forum
Light loss in focussing closer and effective focal length/aperture - Photo.net Nikon Forum

70-200mm AF-S VR II Lens Review by Thom Hogan
*
Marked 200mm on the new 70-200 VFR-II Nikkor zoom is really:
1.4m>>>134mm
2m>>>>147mm
3m>>>>164mm
5m>>>>176mm
10m>>>186mm
Infinity>>192mm


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## clanthar (Sep 2, 2010)

For a simple lens (designed so that the nodal point is at the center of the lens) the focal length increases as you focus the lens on increasingly closer subjects. The lens will have a focal length at infinity that is fixed. Let's make it practical:

You have a 150mm lens on a 4x5 camera. Point the camera at the mountains and focus the lens and the distance from the center of the lens to the film will be 150mm. (At that point the f/stops for the lens can be calculated as: f number = focal length/diameter of the aperture. Let's assume the maximum diameter of the aperture then is 26.5 mm. The lens then is a 150mm f/5.6).

As you focus the lens on increasing closer subjects it physically moves away from the film. If this is a simple lens then the elements of the lens remain in a fixed relationship. Focused on a subject 10 feet from the camera the lens will be approx. 160mm from the film. It will not be a 160mm lens at infinity but in this case its focal length will be 160mm -- you can hold up a ruler if you have to.

Focus this lens at a subject 2 feet away and the lens will be 265mm from the film. It will have a focal length of 265mm. (AND it's fixed maximum aperture of 26.5mm means that the lens will be set at f/10 when the inscribed setting on the f/stop ring is 5.6. This is why it's helpful to think of focal length in this way.)

In the end this get's down to definition of terms. I'm defining focal length as no more and no less than the Webster dictionary definition: "focal length: the distance from the optical center of a lens or curved mirror to the point where light rays from a distant object converge." An understanding that takes that literally works well in the practice of photography.

Joe


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## Helen B (Sep 2, 2010)

clanthar said:


> In the end this get's down to definition of terms. I'm defining focal length as *no more and no less* than the Webster dictionary definition: "focal length: the distance from the optical center of a lens or curved mirror to the point where light rays from a distant object converge." An understanding that takes that literally works well in the practice of photography.



That is a correct definition. The idea that the focal length changes as the whole lens is simply moved as a unit is not correct, and is a cause of confusion.

Best,
Helen


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## AdrianC (Sep 2, 2010)

GaryPolter said:


> clanthar said:
> 
> 
> > Yes. The focal length does change as you focus the lens on subjects increasing closer to the camera.
> ...



As I said, there are *two* rings around the lens. One controls the focal length, one the focus point. You use focus ring to decide what you want to have in focus. 

Also, if its a 110mm prime lens, then its focal length will not change. It will always be 110mm. 

Do you happen to own just a kit lens? Take your camera, and examine it closely. You have the big ring around the lens. When you turn that you will "zoom". Now set the lens in manual focusing mode, grab the outer end of the lens, and turn it. Not the zoom ring, just the end of the lens. Your focus will change. (Note, this should move very smoothly. If it feels like its stuck, do NOT force it to turn.)


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## clanthar (Sep 2, 2010)

Helen B said:


> clanthar said:
> 
> 
> > In the end this get's down to definition of terms. I'm defining focal length as *no more and no less* than the Webster dictionary definition: "focal length: the distance from the optical center of a lens or curved mirror to the point where light rays from a distant object converge." An understanding that takes that literally works well in the practice of photography.
> ...



Looks like maybe agreeing to disagree is our option out here. I of course would say that not understanding how and why the focal length changes is what causes confusion. 30 years ago in a classroom I tried to explain to a group of students that as they focused the camera ever closer the f/stop was changing even though it was (like the focal length) engraved into the lens barrel. f/stop = focal length/aperture diameter. When I gave them that formula and a tape measure and told them to measure the focal length the confusion went away.

Take Care,
Joe


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## Helen B (Sep 2, 2010)

Derrel said:


> Marked 200mm on the new 70-200 VFR-II Nikkor zoom is really:
> 1.4m>>>134mm
> 2m>>>>147mm
> 3m>>>>164mm
> ...



It would be an interesting exercise to mount that lens onto bellows, set the focus ring to infinity and the zoom to the nominal 200 mm then rack it out to the same magnification that is achieved at 1.4 m with the lens in 'normal' use. The image distance can then be measured (bellows flange-flange distance plus 192 mm) and the focal length calculated. One would expect that it is still 192 mm.

Best,
Helen

Edit: I was curious to know how Thom calculated those 'effective focal lengths' because it isn't straightforward. He appears to have used the formula
_[FONT=Verdana, Arial, Helvetica, sans-serif]"You can calculate the focal length of a lens at its closest focus distance by using the formula *minimum_focus / ((1/reproduction_ratio) + reproduction_ratio + 2)*."[/FONT]_

It should always be remembered that that formula applies only when the nodal space is zero or very close to zero. It often isn't for a zoom, telephoto or retrofocus lens. The assumption that it is zero when it isn't zero in reality will not have much effect when applying the formula on distant subjects, but the closer you get the more the error grows.


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## Helen B (Sep 2, 2010)

clanthar said:


> Looks like maybe agreeing to disagree is our option out here. I of course would say that not understanding how and why the focal length changes is what causes confusion. 30 years ago in a classroom I tried to explain to a group of students that as they focused the camera ever closer the f/stop was changing even though it was (like the focal length) engraved into the lens barrel. f/stop = focal length/aperture diameter. When I gave them that formula and a tape measure and told them to measure the focal length the confusion went away.
> 
> Take Care,
> Joe



Joe,

I have no confusion about why the image distance changes, why the _effective aperture_ changes and why the focal length stays the same as long as the lens moves as a unit. I think that you have been teaching your students using optical terminology that is not in agreement with normal terminology in photographic optics. That can be a cause of confusion, as shown in this thread. Had you taught what effective aperture really is, you would not have had to invent the idea that the focal length changes.

Best,
Helen


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## clanthar (Sep 2, 2010)

Helen,

I'm not confused either. I understand that I'm not using common terminology, but I did not invent it (thanks though). I learned a very long time ago that this way of thinking about it can be useful -- got it from this guy Ernst Wildi at a seminar in a session about macro photography. What I've learned is that having multiple ways to understand things usually helps rather than confuses. I say "effective aperture" to my students as well and I also show them how to manage bellows factor by measuring magnification -- the more ways to think about it the better. I found the way Mr. Wildi explained was very useful.

Joe


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## Derrel (Sep 2, 2010)

Helen B said:


> Derrel said:
> 
> 
> > Marked 200mm on the new 70-200 VFR-II Nikkor zoom is really:
> ...



The photographs show a 29% loss of focal length compared with the older 70-200mm VR Nikkor....all one has to do is look at the images to see that there is a HUGE loss of focal length as the lens is focused closer...the mannequin head is vastly,vastly smaller with the new lens....134mm is a far cry from 200mm, or even the 182mm of the old lens at MFD...

SOme lenses, as he mentions, like the 18-200 VR Nikkor lose a HUGE amount of focal length when focused closer....the Tamron 90mm f/2.8 AF-SP drops to ~73mm at 1:1..

The Nikkor 50mm f/1.8 AF-D OTOH, increases in FL to ~59mm from its normal Infinity focal length of 51.6mm when racked out to its .45m MFD...

70-200mm AF-S VR II Lens Review by Thom Hogan

I'm still a bit unclear on how/what/why the OP is asking such an odd question...it would seem that a few minutes actually focusing on close-up items would answer his questions.


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## GaryPolter (Sep 2, 2010)

Derrel said:


> I'm still a bit unclear on how/what/why the OP is asking such an odd question...it would seem that a few minutes actually focusing on close-up items would answer his questions.



I wish I could do this, but I don't actually have an SLR camera.  I came here because I believed (and was proven correct) that all of you are very knowledgeable about lenses.

The main purpose of me asking this question is because I'm trying to create a realistic depth of field technique for a 3D computer application, but I was not clear on what the difference between focal length and focus was.  All literature I've read on depth of field assumes knowledge of these two items.


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## Helen B (Sep 2, 2010)

As far as modeling a simple lens goes, and for applying the simple 1/f = 1/u + 1/v formula you mentioned in your original post, you can safely assume that the focal length is constant. This applies to all lenses that focus as a unit, without exception. Using any other theory will get you into trouble if you try to apply optical formulae.

The complication caused by lenses that alter the arrangement of their internal elements as they focus is probably not worth incorporating into a model, unless you wish to model the behaviour of a particular lens. In that case you would have to have information about the way that particular lens changes its focal length, because there are no fixed rules.

Best,
Helen


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## GaryPolter (Sep 2, 2010)

I think something finally clicked in my brain.  So as Helen said, the thin lens equation assumes a fixed focal length.

So let's say I tell my lens to have some fixed focal length of 50mm.  This means for "infinitely" far objects I need to have the lens 50mm away from the image sensor.  If an object is 1000mm away, then to focus it, the lens will move, but the focal length stays the same.  Put another way, the focal ring will only move the lens closer/further from the image sensor.  When I use the focal ring to move the lens 52.6mm away from the sensor then this image will be in focus.

To ask if other objects will be in focus is not a good question because for that I'll need to calculate the depth of field which requires other values such as aperture.


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## Helen B (Sep 2, 2010)

GaryPolter said:


> I think something finally clicked in my brain.  So as Helen said, the thin lens equation assumes a fixed focal length.
> 
> So let's say I tell my lens to have some fixed focal length of 50mm.  This means for "infinitely" far objects I need to have the lens 50mm away from the image sensor.  If an object is 1000mm away, then to focus it, the lens will move, but the focal length stays the same.  Put another way, the focal ring will only move the lens closer/further from the image sensor.  When I use the focal ring to move the lens 52.6mm away from the sensor then this image will be in focus.
> 
> To ask if other objects will be in focus is not a good question because for that I'll need to calculate the depth of field which requires other values such as aperture.



Yes, you have got it. It is not just theoretical thin lenses that maintain their focal length. All lenses that focus as a unit (ie there is no change in the relative positions of the elements within the lens) maintain constant focal length. The formula 1/f = 1/v + 1/u applies to those lenses as well, if u and v are measured from the correct points. The object distance must be measured from the front (or first) nodal point and the image distance must be measured from the rear (or second) nodal point. In most cases you probably don't need to know the exact location of the first nodal point  for your particular application. 

As an aside, the focus markings on lenses are usually made for the distance from the image plane, call it D. If the distance between the nodal points is s, measured in the direction of light travel, then

D = u + v + s 

Best,
Helen


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