What is "focal length" REALLY?

I always come across different definitions of "focal length". I was thinking it meant the range of focus (ie, a lens that can focus on something 1" away has a minimum focal lengh of 1"), but then the guy at the camera store said my 18-200mm lens has a max focal length of 200mm, and NOW, I looked it up via Google (a search for "define: focal length") and got BOTH those definitions.

( http://www.google.com/search?hl=en&q=define%3A+focal+length&btnG=Google+Search&aq=f&oq= )

1 - The measurement that determine the magnification and field of view of a lens. Expressed in mm.
2 - focal distance: the distance from a lens to its focus

3 - The distance between the center of a lens (the principal point) and its focal point.

What's the deal? What does it really mean?

--
http://www.deefrag.com

If you reverse the order of those definitions, you'd have the correct sequence; start with the strict definition from physics, and expand toward the vernacular. Keep in mind that the simple definition(dist from lens to it's focus) applies to simple lenses, and also at infinity focus only. Hold magnifying glass up to a window with an outside view, and image the scene outside onto a piece of white paper in your other hand...there...you just measured the focal length of that lens.
--
-KB-

Dario D said:

I always come across different definitions of "focal length". I was
thinking it meant the range of focus (ie, a lens that can focus on
something 1" away has a minimum focal lengh of 1"),

Click to expand...

Generally, lenses with longer focal lengths cannot focus as closely as short focal-length lenses, however these parameters are not tightly coupled and there is a wide variation in closest-focus distance amongst lenses of similar focal lengths. This is why some lenses are designated "macro" while others are not.

Dario D said:

but then the guy
at the camera store said my 18-200mm lens has a max focal length of
200mm, and NOW, I looked it up via Google (a search for "define:
focal length") and got BOTH those definitions.
1 - The measurement that determine the magnification and field of
view of a lens. Expressed in mm.
2 - focal distance: the distance from a lens to its focus
3 - The distance between the center of a lens (the principal point)
and its focal point.

Click to expand...

Practically speaking, definition 1) is most important. Although neither magnification nor field of view are dependent solely upon lens focal length (they also depend on subject distance and imager size, respectively), these are usually the most important considerations to a photographer.

Given a subject which is distant, or at least not very close to the camera, the subject magnification will be closely proportional to the lens focal length. To an excellent approximation, the magnification (ratio of image height to subject height) will be equal to the lens focal length divided by the subject distance.*

For example, consider a subject which is 2m tall, and standing 100m away from the camera. With a 12mm lens, the image height will be 2m x 12mm/100m, which is 0.24mm - very tiny. Longer lenses produce proportionally larger images of our subject:
24mm lens: 0.48mm image
50mm lens: 1.0mm image
85mm lens: 1.7mm image
135mm lens: 2.7mm image
200mm lens: 4mm image
400mm lens: 8mm image
800mm lens: 16mm image

If you are using a 24mm x 16mm image sensor, in the last case the subject would use the full sensor height if the camera is held horizontally, so the field of view is 2m high x 3m wide. With the shorter lenses, field of view grows in inverse proportion to focal length. The 200mm lens has an 8m x 12m FOV, the 50mm lens has a 32m x 48m FOV, etc.

• Strictly, magnification is the lens-to-image distance divided by lens-to-subject distance. This distinction becomes significant only for close subjects.

Dario D said:

What's the deal? What does it really mean?

Click to expand...

The focal length of a lens is a physical property of that lens that describes its most important optical properties. Specifically, it is used in the formula:

1/F = 1/O + 1/I

Where F is the Focal length, O is the distance from the lens to the Object, and I is the distance from the lens to the Image. It turns out that this definition is all you need to figure out how much you need to move a lens to get a specific object in focus, how large an image it will produce when it is in focus, and the like. The most important relationship that you as a photographer need to know is that for a distant object (i.e. where O > > F ≈ I), the size of an image is directly proportional to the focal length. The image of an object projected by a 50mm lens is twice as big as the one projected by a 25mm lens and half the size of one projected by a 100mm lens.

For real world lenses there are three complicating factors. The most obvious is that zoom lenses change their focal length when you zoom them. Less obvious is that the distances O and I aren't measured from the center of the lens. They're measured from points called the principal points of the lens. Those points are not necessarily the same (i.e. O is measured from a different point on the lens from I), and they aren't necessarily even inside the lens. Finally, and most confusingly, is that some lenses actually change their focal length as they focus, so that their listed focal length is only 100% valid when they're focused to infinity. The change in focal length is usually minor, but it can be significant when focusing very close.
--

As with all creative work, the craft must be adequate for the demands of expression. I am disturbed when I find craft relegated to inferior consideration; I believe that the euphoric involvement with subject or self is not sufficient to justify the making and display of photographic images. --Ansel Adams

Dario D said:

I always come across different definitions of "focal length". I was
thinking it meant the range of focus (ie, a lens that can focus on
something 1" away has a minimum focal lengh of 1"), but then the guy
at the camera store said my 18-200mm lens has a max focal length of
200mm, and NOW, I looked it up via Google (a search for "define:
focal length") and got BOTH those definitions.

(

http://www.google.com/search?hl=en&q=define%3A+focal+length&btnG=Google+Search&aq=f&oq= )
1 - The measurement that determine the magnification and field of
view of a lens. Expressed in mm.
2 - focal distance: the distance from a lens to its focus
3 - The distance between the center of a lens (the principal point)
and its focal point.

What's the deal? What does it really mean?

--
http://www.deefrag.com

Click to expand...

I always understood it to mean the distance from the focal plane to the rear element of the lens like in a rangefinder (Contax G2 or Leica). So it is xyz millimeters. I am thinking with a zoom lens the distance changes from the focal plane to the rear element as you zoom. Perhaps with an SLR since you are looking through the lens rather than sighting over it even like a P&S film camera or the fore mentioned Leica/Contax when P&S did not have an lcd

ryan2007 said:

I always understood it to mean the distance from the focal plane to
the rear element of the lens like in a rangefinder (Contax G2 or
Leica). So it is xyz millimeters. I am thinking with a zoom lens
the distance changes from the focal plane to the rear element as you
zoom. Perhaps with an SLR since you are looking through the lens
rather than sighting over it even like a P&S film camera or the fore
mentioned Leica/Contax when P&S did not have an lcd

Click to expand...

While back focus is important (you need some to keep the mirror from whacking the lens in an SLR) it is in no way related to the focal length. Focal length is a geometric property of a lens that determines how it scales objects. It's simple for simple lenses (for a thin lens, it's, the distance from the lens to the focal plane when the lens is focused at infinity) and complicated for comples lenses, which is what we all use.

For example, I have no idea what the focal length of my MP-E 65 lens is when it's set at 5:1 macro. Absolutely no idea. But the back focus is about 50 mm.

--
Leonard Migliore

Dario D said:

I always come across different definitions of "focal length". I was
thinking it meant the range of focus (ie, a lens that can focus on
something 1" away has a minimum focal lengh of 1")

Click to expand...

I think your terminology is a bit confusing. Range of focus is usually refers to depth of field and whilst has a relation to lens focal length does not define it. The focal length is the distance from the lens the focal plane (i.e. the plane where projected image will be in focus) when focussed at infinity (i.e. all distant objects will be in focus). This is not a range of planes but a single plane which is where the camera sensor of film usually placed.

Now from where this diatance is actually measured (nodal point, entry point, etc) is a good question and I don't have an answer to this apart from when a lens is single element one.

I can however say this - it may not be an entry point (fron of the lens) in all cases because the lenses such as Sigma 24-70mm f/2.8 is extending towards its shortest end of 24mm and contracting towards its longest end of 70mm.

Having read a few articles (mostly on Wikipedia and publications it refers to), it appears to me that focal length seems to be simply a distance from the entrance pupil of the optical system to the focal plane when focussed at infinity (i.e. all the distant subjects are in focus on the focal plane).

The entrance pupil itself for an optical system seems to be virtual (see http://en.wikipedia.org/wiki/Entrance_pupil ) and citing the article on Wikipedia: "depending on the lens design, the entrance pupil's location on the optical axis may be behind, within or in front of the lens system, or even at infinity in the case of telecentric systems".

One of the problems of trying to answer questions like this is that it's tough to include a diagram that helps in the explanation. I think that the Wikipedia article on Focal Length may help explain both what 'focal length' means in theoretical terms and how it is used in photographic parlance:
http://en.wikipedia.org/wiki/Focal_length

Dario D said:

I always come across different definitions of "focal length".
1 - The measurement that determine the magnification and field of
view of a lens. Expressed in mm.
2 - focal distance: the distance from a lens to its focus
3 - The distance between the center of a lens (the principal point)
and its focal point.

Click to expand...

This can get a bit complicated, and I'm not an optical engineer, so I'll use simple examples along with a bit of history. I welcome any corrections to this description.

Take a simple single element lens (like a magnifying glass) and focus it on an object at infinity. The distance between the center of the lens and the focal plane (film or digital sensor) is the focal length. Longer focal lengths have higher image magnification, and shorter focal lengths has less image magnification.

Now take a modern, multi-element lens. The simple example above falls apart, because there are multiple pieces of glass - which one do you measure to? Each lens element has its own focal length, but when you combine them, you get an effective focal length that has an equal magnification (and field of view) to a simple lens. Simply stated, if your multi-element lens has the same image magnification as a single-element 135mm lens, then it is considered to be a 135mm FL lens.

If you measure 135mm from the focal plane (where the film or digital sensor is located), you have reached the "entrance pupil" of the lens. This point is, in effect, the location where the center of a single-element lens would be located. You may discover that this point is actually an empty space (gap between lens element).

On long lenses, the entrance pupil is generally out toward the front region of the lens. This is not the case for short FL lenses, however. A simple 14mm lens would need to located 14mm from your digital sensor, which would put it inside the camera's mirror box. That would cause the mirror to crash into it, and make it impossible to use. In fact, Nikon had a 6mm fisheye lens that required you to lockup the mirror before you could mount the lens.

http://www.mir.com.my/rb/photography/companies/nikon/nikkoresources/6070nikkor/fisheyes/6mm56.htm

Retrofocus lenses were developed, which pushed the lens outside the body, then added a negative element to extent the distance from the lens to the film plane. With this design, the back focus distance (rear lens to focal plane) was longer than the focal length. This is how your 18-200mm lens can sit outside your camera body, yet deliver a focal length of 18mm.

Here's the point to remember - in effect, the focal length simply indicates how much image magnification you'll get. The longer the FL, the more magnification you'll get.

My goal with to offer a simple explanation. I invite any optical engineers to correct and/or clarify my statements.

--
Ken Elliott
Equipment in profile.

MasterOfGoingFaster said:

Now take a modern, multi-element lens. The simple example above
falls apart, because there are multiple pieces of glass - which one
do you measure to? Each lens element has its own focal length, but
when you combine them, you get an effective focal length that has an
equal magnification (and field of view) to a simple lens. Simply
stated, if your multi-element lens has the same image magnification
as a single-element 135mm lens, then it is considered to be a 135mm
FL lens.

If you measure 135mm from the focal plane (where the film or digital
sensor is located), you have reached the "entrance pupil" of the
lens. This point is, in effect, the location where the center of a
single-element lens would be located. You may discover that this
point is actually an empty space (gap between lens element).

Click to expand...

No, what you are describing is called the rear principal plane. The entrance pupil, which is the apparent location of the lens's limiting aperture, can be anywhere, even out at infinity.

http://en.wikipedia.org/wiki/Cardinal_point_ (optics)

--
Leonard Migliore

Thanks for pointing out my error. Its not my field and I figured my layman's description would have at least one error.
--
Ken Elliott
Equipment in profile.

Distance from the rear nodal point to the focal plane.
--
http://www.pbase.com/lanef/galleries

ryan2007 said:

Dario D said:

I always come across different definitions of "focal length". I was
thinking it meant the range of focus (ie, a lens that can focus on
something 1" away has a minimum focal lengh of 1"), but then the guy
at the camera store said my 18-200mm lens has a max focal length of
200mm, and NOW, I looked it up via Google (a search for "define:
focal length") and got BOTH those definitions.

(

http://www.google.com/search?hl=en&q=define%3A+focal+length&btnG=Google+Search&aq=f&oq= )
1 - The measurement that determine the magnification and field of
view of a lens. Expressed in mm.
2 - focal distance: the distance from a lens to its focus
3 - The distance between the center of a lens (the principal point)
and its focal point.

What's the deal? What does it really mean?

--
http://www.deefrag.com

Click to expand...

I always understood it to mean the distance from the focal plane to
the rear element

Click to expand...

The way the image is projected on your focal plane is: Right goes left and left goes right, top goes bottom, bottom goes top. So where those lines intersect to the focal plane is the focal length.

http://www.pbase.com/lanef/galleries