Focal length - does this change when a camera focuses?

[sreelalts]

Hello everyone,

For those who are interested in optics behind the camera, I have a basic (stupid? ) question which is bugging me for some time even after trying to figure out the answer from internet...

Let me limit this question to full frame camera and avoid the crop factor discussion. We all know, that focal length is the distance between the lens and the sensor/film. Now let us consider a 200 mm lens. This means that the focal length of lens is 200 mm - or the distance between the lens and sensor/film is 200 mm, by definition. Since we use a combination of lens elements within the barrel, the physical distance may be less than 200 mm, but the effective distance will be the same 200 mm.

Now let us take a picture! The subject can be placed any where between lens and infinity. While focusing the subject, the lens elements move internally to get a sharp image of the subject. In otherwords, we are changing the focal length!! It is also known that if the subject is placed far away, the reflecting rays will be more parallel and hence the focal length will be short (or image will be obtained closer to the lens plane). Contrary to this, of the subject is close to the lens, reflected rays from the subject are more inclined, and hence the focal length will be more or the distance between the lens and sensor will be more (for this reason, a 200 mm lens cannot focus on very near objects which requires very large focal length beyond the physical size of the barrel). Since the sensor plane is fixed in the camera, the lens moves instead of moving the sensor to focus on near or far subject. Ooops! We are still talking of the same 200 mm focal length lens!!
In the case of zoom lenses we do two operations. 1) Zoom in or out to decide on the magnification and field of view 2)Focus on the subject, once we fix zoom
So what is the difference? Which one is the focal length? Are we mistaking zoom for focal length?
I know, even without knowing this we can enjoy our camera and shoot good pictures, but just for the academic interest

Can any one help me please?

[Andy]

The focal length marked on a lens is only right when it's focussed on infinity and is the distance from the rear nodal point of the lens to the focal plane in the camera.

...or at least close enough, there's usually a little difference between quoted focal length and actual focal length.

The focal length of some lenses changes significantly with focus though - e.g., Canon 100mm macro is apparently closer to 70mm when it's at minimum focus.

What's the difference between the focus ring and the zoom ring on a zoom lens? It depends on the zoom! Parfocal lenses do not change the focus distance as you zoom, only the focal length changes. Changing the focus distance changes the focal length slightly, moving the zoom effects the actual focal length significantly so no, I don't think we are mistaken.

[Steaphany]

Lets explain this with a simple lens, i.e. a single convex optical element.

Here is a diagram:



and a formula:



Lets use your 200mm as the value of f

Lets start with the object being positioned 1000mm from the lens, S1, and plug these values into the equation and solve for S2, which turns out to be 250mm. Hmmm - that a bit more than 200mm.

Well, try again, this time S1 being 500mm and now S2 is 333.3mm, Wow even further from the focal length.

Now try S1 at 2000mm, S2 becomes 222.2mm. Hmmm, well it's now heading towards the focal length. But have you noticed the pattern ?

As the distance between the object and lens decreases, the lens to image plane, S2, increases.

Lets look at a special case, when S1 in infinite. Here the reciprocal becomes 0 and S2 finally reaches the same value as the focal length.

Here is another special case, when S1 is equal to 2f, 400mm, solving for S2 yields 400mm. Hmmm, a 1 to 1 Macro. This is why Macro tubes work, all that's needed to focus closer is an increase between the lens and image plane.

Having the object much closer than 2f is not practical with a camera, but that's when your entering the realm of microscopes.

There is no point having S1 becoming close to or at the same value as f since that pushes S2 towards infinity, only useful in film projectors. Also, if S1 is less than f, you end up with no projected image and the lens starts acting like a magnifying glass.

[sreelalts]

Thank you Steaphany & Andy for your time.
Now, it gives more insight into the issue...

@Steaphany,
Based on the thin lens equation as you have stated, f is nothing but an optical property a lens, what is going to vary is S1 and S2. Am I correct?
(f is determined by the radius of curvature, refractive index and thickness of the lens)
In other words, focal length is always fixed!

Hang on, since we are not dealing with a single lens element, it may be possible to vary the f (focal length) by moving around the various lens elements within the barrel.

My guess is that we might be changing S2 by turning the zoom ring and changing the f value by turning the focus ring

... ooopS! did i go very far?

Any opinion?

[sreelalts]

@ Andy,

You are right in stating that - "focal length marked on a lens is only right when it's focussed on infinity"
Because, for objects at infinity, the light rays will be parallel and hence they will converge exactly at the focal length. S2=f (special case mentioned by Steaphany)

My confusion here is that, in many articles about photography in internet, we mention the distance between the lens and image plane as the focal length - actually it is NOT!! It is clear from the diagram provided by Steaphany.

[Steaphany]

@Steaphany,
Based on the thin lens equation as you have stated, f is nothing but an optical property a lens, what is going to vary is S1 and S2. Am I correct?
(f is determined by the radius of curvature, refractive index and thickness of the lens)
In other words, focal length is always fixed!

Hang on, since we are not dealing with a single lens element, it may be possible to vary the f (focal length) by moving around the various lens elements within the barrel.

My guess is that we might be changing S2 by turning the zoom ring and changing the f value by turning the focus ring

... ooopS! did i go very far?

You are right on and on your way towards a career as an optical system design engineer.

Now to the next step, multiple lens elements:



Given two lenses, of focal lengths f1 and f2 separated by distance d, this formula will give you the combined focal length.

Lets say f1 is 200mm, f2 is 100mm, and d is 50mm, then the combined optical system would have a focal length of 80mm.

Lets turn the Zoom ring and shift the spacing to 75mm, now the combined focal length is 88.89mm

Turning the Zoom ring in the opposite direction to a spacing of 25 yields 72.73mm, Wow we have a 1.2X Zoom lens.

In modern optics, designers have far more complex equations and performance trade offs to balance out. The mechanical system may need to shift the positions of multiple elements simultaneously, and the ratio of the shift may differ for each element. Both positive and negative elements need to be combined to compensate for Chromatic aberration because the index of refraction is rarely constant and does vary with the wavelength of light. ( This is why a prism makes a spectrum, the bending of light through the prism is dependent of the index of refraction and index of refraction is dependent on wavelength )

I have several "put you to sleep" texts on optical system design that goes into these concepts in far greater detail than I touched upon here. Try finding the "Handbook of Optics" Volume I, Fundamentals, Techniques, & Design, Edited by Michael Bass, published by McGraw Hill, ISBN 0-07-047740-X. I have the second edition published in 1995 along with Volume II Devices, Measurements, & Properties. Chapter 1 General Principals of Geometric Optics contains 109 pages of formula on this very subject plus the whole 2.75" thick book pretty much addresses everything an optical systems designer needs to know. I keep these books on my "Fun Subject" shelf of books.

and just as an added bonus, and because you brought it up, here is the Lensmaker's equation:



where

f is the focal length of the lens
n is the refractive index of the lens material, remember this changes with wavelength
R1 is the radius of curvature of the lens surface closest to the light source
R2 is the radius of curvature of the lens surface farthest from the light source
d is the thickness of the lens (the distance along the lens axis between the two surface vertices).

-=-=-

I just did a quick search and found the

Handbook of Optics Volume I Fundamentals, Techniques, &Design

is available at a nice cheap price, used for $71.94US. They don't have new copies available since the third edition is due to come out soon.

[sreelalts]

Thanks a lot!
This indeed is useful...

@Steaphany,
I will definitely checkout the book you mentioned... Thank you.

Trying to consolidate the key info which I gained in this discussion:

1. For a 200 mm lens, the image plane will be at 200 mm only when we focus on infinity
2. When we focus a near by subject, the image plane will be placed farther away from 200 mm (eg if S2=600 mm, image plane is at 300 mm from the lens)
3. When we focus a far off subject, image plane will be nearby (eg if S2=6000 mm, image plane is at 206.89 mm from the lens)
4. When we focus at infinity, image plane will be at f (eg if S2=infinity, image plane is at 200 mm from the lens)
5. Turning the zoom ring changes S2. Lesser S2 will give wider field of view or wide angle (FOV) and when we zoom in you increase S2 and thereby narrow the FOV
6. When you turn the focus ring, you change the f value to match with given S1 and S2

Please correct me if I am wrong!
Thank you once more...

[Steaphany]

Do keep in mind that a SLR camera pretty much keeps the distance between the optics and film plane relatively fixed. With some older SLR lenses on newer digital cameras, you have to watch for conflict between elements within the camera body and the rear lens element as the zoom or focus is adjusted.

When you adjust a Lenses zoom, you shift groups of lens elements which yield an "equivalent" angle of view corresponding to the specified focal length. Adjusting the Focus ring shifts other elements which permit a clearly focused image the camera's image plane. If your lens is good, adjusting focus will have, hopefully, no effect of angle of view "zoom". ( I actually have a high quality lens that I used for a focal blended macro composite and found that the image size will vary as the focus ring is adjusted. )

Real flexibility and an understanding of focus comes when you enter the large format camera world. These cameras, ranging from 4"x5" to 16"x20", are still very popular and connect the lens to the film plane by means of a flexible light tight bellows. This permits focus control where you can even specify a plane through your scene where focus can be perfectly maintained through out.

Here is a very cool demonstration which shows the advantages of focal plane control:

Fun With a View Camera – Using Camera Movements to Achieve Your Vision

This article actually shows how fixed lens cameras, SLRs and Point and Shoot, focus the subject with a plane perpendicular to the center line of sight ( Parallel to the film or imager plane ) and how altering the angle of both the lens and image plane allows you to selectively control what is in focus from the scene. ( The Lensbabies are popular because they provide a low cost method to achieve some of this with an SLR )

A point of note regarding a graphic from this article:



Remember that the image projected into the film or imager of a camera is upside down and left-right reversed. So, recalling earlier in this thread where distant objects focus close to the lens and near objects focus far, look at this diagram. The wall being photographed close to the camera, on the left, is projected onto the right side of the image plane which has the lens and image plane angled to achieve the greater distance. Likewise the objects on the distant right get projected to the left side of the image plane with a short distance.

I do recommend that you read this article. Large format photography can really open your eyes and understanding of photographic concepts. ( It will easily spoil you, you'll shoot with your SLR, look at the image and say "I can't get this to focus the way it should be" )

[Dave Humphries]

Just a note to say to anyone wondering how to interpret the white diagram shown in Steaphany's post #8 should click the "Fun with a View Camera" link above the image; all will then be revealed, as they say.

Well worth reading, as per Steaphany's recommendation, to see on a single web page, exactly what all the fuss is about!

A good find Steaphany, thanks,

[rpcrowe]

We tend to call all lenses of longer than "normal" focal length ("normal" focal length is considered 50mm on a full frame camera; shorter on smaller formats and longer on larger formats) "TELEPHOTO". Although this is the modern accepted definition of telephoto, the stricter definition is that a telephoto lens is a lens in which the lens to film distance, when focused at infinity is less than the focal length.

There are few, if any, long focal length lenses produced today which are not telephoto. However these lenses were once very popular and were correctly called "long focus lenses". Some were extremely large because the barrel had to accommodate the focal length distance.

As a example, the size of a 2,000mm lens was at least 2,000mm long.

As I mentioned, a telephoto lens has a physical length shorter than the focal length. As an example, the Canon 400mm f/5.5L lens is only 256mm long.

[sreelalts]

stricter definition is that a telephoto lens is a lens in which the lens to film distance, when focused at infinity is less than the focal length.

Initially I thought this definition is wrong. But checked out the Wikipedia http://en.wikipedia.org/wiki/Telephoto_lens

Thanks for the new info