What makes a lens's focal length?

JeremyLangford · 03-09-2009

I understand that the focal length of a lens is the distance between the lens and the film plane when focused at infinity. But what makes that distance what it is? Why does a 35mm lens focus parallel light rays exactly 35mm away? Is it the circular shape of the glass elements?

rya · 03-09-2009

Are you looking for something like this?:

http://www.saburchill.com/physics/chapters3/0008.html

Camera lenses obviously have multiple elements, but I guess that this is what you are after.

Brian Sweeney · 03-09-2009

The laws of refraction do that. Light bends, and travels at different velocity as it enters a medium with a different index of refraction. The shape of the interface controls the bending.

Best to pick up an elementary physics or optics book on this. Modern lens design is more complex as to the shape and position of multiple elements to get a good image.

Of course, some of us treat optics as if they were Tinker Toys.

My 5cm F2 "Astignar", made from the front half of a J-8 and rear module from a Retina Xenon. Groups spaced to form a 50mm lens, and collimated for the Leica using an I26 mount.

Only one like it in the world, and there will only be one. Now on an M8.

Just to show those computers really do correct aberrations. I did not use a computer for this one....

elshaneo · 03-09-2009

Brian,

That's really awesome !!! You got a unique lens that does output a unique look that I like very much !!!

JeremyLangford · 03-09-2009

Quote:

Originally Posted by Brian Sweeney

The laws of refraction do that. Light bends, and travels at different velocity as it enters a medium with a different index of refraction. The shape of the interface controls the bending.

Best to pick up an elementary physics or optics book on this. Modern lens design is more complex as to the shape and position of multiple elements to get a good image.

So theres plenty of different ways a lens could be made into having a focal length of........let's say 50mm right?

Roger Hicks · 03-10-2009

Quote:

Originally Posted by JeremyLangford

So theres plenty of different ways a lens could be made into having a focal length of........let's say 50mm right?

Dear Jeremy,

Yup. The simplest would be a magnifying glass that would focus the sun into a burning spot at 2 inches/50mm from the middle of the lens. Add a second lens, cemented to the first (a 'cemented doublet'), and you can lose some of the flaws and aberrations that you have if you use only a single lens. Use two of these cemented pairs, arranged symmetrically on either side of the diaphragm, and you can do even better. That's the origin of symmetrical lenses.

Alternatively, use three air-spaced glasses and you have a Cooke Triplet. Substitute a cemented doublet for one of these and you have a Tessar (or Elmar). Substitute cemented doublets or even triplets and you've got Sonnars.

More glasses are used for (a) more speed (b) wider coverage (c) better correction (higher sharpness, less distortion) or for any combination of these. Then there are tele lenses (more glasses used behind the image-forming group to physically shorten the lens) and reverse-tele or Retrofocus lenses (more glasses used in front of the image-forming group to increase the distance between the rear glass and the film or sensor, to allow room for a reflex mirror).

Neither tele nor Retrofocus construction improves image quality -- both are matters of physical convenience, not optical quality -- and Retrofocus makes the lens bulkier and more expensive, which is why rangefinder wide-angles can be any combination of smaller or cheaper or faster or better.

Cheers,

Roger

ClaremontPhoto · 03-10-2009

Roger: I understand this stuff already, and that is the clearest I have ever seen it explained.

Wiyum · 03-10-2009

Quote:

Originally Posted by ClaremontPhoto

Roger: I understand this stuff already, and that is the clearest I have ever seen it explained.

Roger,

I don't understand this stuff well at all, and I thank you for your wonderful explanation.

If your expertise is willing to go deeper, I've been told that an f/stop is the relationship between the focal length and the physical size of the aperture. I've also been told that it isn't the physical size of the aperture but the "virtual" size of the aperture as viewed through the front element. Can you elaborate and/or bring your soft touch to an explanation? I've never been able to figure this out.

Brian Sweeney · 03-10-2009

Quote:

Originally Posted by JeremyLangford

So theres plenty of different ways a lens could be made into having a focal length of........let's say 50mm right?

Roger concisely summed up lens design spanning decades in a few paragraphs.

Most modern "fixed focal length" lenses are really two fixed focal length lenses placed back-to-back. The "front lens" and "rear lens" can each form an image on their own. The spacing between the front and rear lens can be adjusted to control the focal length of the "composite" lens. The spacing to the film plane controls the focus of the composite lens. The precise design of the front and rear lenses controls the aberrations produced. That's why my lens has such unusual behavior, the "front lens" and "rear lens" are not designed to cancel each other's aberrations. If you take two identical lenses, place them back-back (or front to front), they cancel each others aberrations.

Some more photo's of the "Astignar", as this lens shows astigmatism like none other.
http://ziforums.com/showthread.php?t=138

Roger Hicks · 03-10-2009

Quote:

Originally Posted by Wiyum

. . . I've been told that an f/stop is the relationship between the focal length and the physical size of the aperture. I've also been told that it isn't the physical size of the aperture but the "virtual" size of the aperture as viewed through the front element. Can you elaborate and/or bring your soft touch to an explanation? I've never been able to figure this out.

To be honest, the 'virtual' aperture is so complicated that I'm not sure understand it either. The best explanation I can give, based on what I think I understand, is that the effective size of the aperture is magnified or diminished by its position relative to the various glasses in the lens.

Thus, imagine removing the aperture from the middle of the lens, and putting it in front. A hole that size would lead to severe vignetting. In the middle, it doesn't.

A more useful concept, in any case, is the T-stop, which is based on the actual measured transmission (hence T/stop), not on a caculation of the relationship of the aperture hole and the focal length, with no allowance for flare and absorbtion. A T-stop is always less than the calculated F-stop, so (for example) f/2 might at best be f/2.2.

For those who don't already know, the reason for using f/stops (or better still, T/stops) is because they are independent of focal length. Thus, an f/2 lens is f/2 regardless of focal length, so an f/2 21mm will need the same exposure time under given illumination with a given film speed as an f/2 100mm.

Cheers,

Roger

maddoc · 03-10-2009

Thanks a lot for the information so far ! Now I have a question, regarding change of focal length (of prime lens) when changing focus from closest distance to infinity. Why does the focal length, e.g. for a 50mm lens, change from ~52mm to 50mm while changing focus ?

JeremyLangford · 03-10-2009

Quote:

Originally Posted by maddoc

Thanks a lot for the information so far ! Now I have a question, regarding change of focal length (of prime lens) when changing focus from closest distance to infinity. Why does the focal length, e.g. for a 50mm lens, change from ~52mm to 50mm while changing focus ?

I thought that it doesn't change because focal length is only calculated when focused to infinity.

Gumby · 03-10-2009

Quote:

Originally Posted by ClaremontPhoto

Roger: I understand this stuff already, and that is the clearest I have ever seen it explained.

Roger probably copied that from a book he already wrote.

Al Kaplan · 03-10-2009

The focal length doesn't change as you focus closer but the increase in distance from the film gives you a narrower angle of view. It also reduces the effective f-stop because the diaphragm isn't as close to the film.

T-stops came about back in the days when motion picture cameras had several lenses mounted on a turret instead of a single zoom lens. Even if they all had the same f-stop they wouldn't all transmit the same amount of light. Any lens set for T-5.6 transmits the same amount of light as any other lens set at T-5.6. The lenses are usually also marked in conventional f-stops, which are useful in determining depth of field. Modern cameras with through the lens metering pretty much do away with the problem of different lenses transmitting varying amounts of light at a given f-stop.

Roger Hicks · 03-10-2009

Quote:

Originally Posted by Gumby

Roger probably copied that from a book he already wrote.

No, it's quicker to re-write it from scratch. In any case, I don't think I've ever thought of explaining it before, because I'm no optical expert. That's why I copped out on f/stops, and why I haven't previously attempted the bit about the change in coverage with focusing. The harder I thought about it, the more I suspected that I was thinking backwards: on the model I was using, coverage should increase as you focus closer. But then, I've got one of those nasty coughs/colds that stops you thinking clearly.

Try this for size, though.

Consider a fully symmetrical lens, with the nodal point (from which you measure the focal length) bang in the middle.

As you focus closer, the effective focal length increases because the nodal point is further from the film or sensor. In other words, a 50mm lens becomes (let us say) a 55mm lens; hence a narrower angle of view.

Hold on: I think I see where I was thinking backwards with the other model.

Think of a pair of scissors. The hinge is the nodal point; the blades on one side, and the gap between the handles on the other, represent the angle of view.

Put an object -- a film canister, say -- half-way down the blade of the scissors and close them (gently so it doesn't cut -- or use a bottle neck). Now start sliding it outwards, away from the hinge. The angle between the blades (and the handles) goes down: that's the angle of view. This is what happens as you move the nodal point away from the film or sensor (the film canister away from the hinge).

At maximum extension (minimum focusing distance) the angle is smallest, therefore the field of view is smallest.

Hope that makes sense. I really don't feel up to the 1/f, 1/v, 1/u stuff at the moment, which I'd need to do in order to convince myself I'd got it right.

Tashi delek,

Roger

mabelsound · 03-10-2009

Damn, Brian, that Astignar is wild. I love it.

Al Kaplan · 03-10-2009

The scissors analogy is brilliant, Roger!

Roger Hicks · 03-10-2009

Quote:

Originally Posted by Al Kaplan

The scissors analogy is brilliant, Roger!

Hey, Al, if it fools you, it must be convincing. Or possibly even right!

Thanks for the kind words.

Tashi delek,

R.

sevo · 03-10-2009

Quote:

Originally Posted by Roger Hicks

Consider a fully symmetrical lens, with the nodal point (from which you measure the focal length) bang in the middle.

As you focus closer, the effective focal length increases because the nodal point is further from the film or sensor. In other words, a 50mm lens becomes (let us say) a 55mm lens; hence a narrower angle of view.

Almost right. The focal length is a constant, defined at infinity. The distance to the image plane however increases in proportion to the drecreasing distance to the object plane. At 1:1 magnification, a lens of 50mm focal length would have 100mm image and object distance each, with both side effects of going from 50 to 100mm - the increased coverage (image circle) a 100mm lens of a identical scaled design would have at infinity, and a corresponding narrower angle in relation to the constant image size.

Al Kaplan · 03-10-2009

...and at 1:1 you'd lose two stops of light reaching the film because of the law of inverse squares.

Wiyum · 03-10-2009

Quote:

Originally Posted by Al Kaplan

Modern cameras with through the lens metering pretty much do away with the problem of different lenses transmitting varying amounts of light at a given f-stop.

Of course, modern motion picture cameras, as then, don't use through the lens metering (I've seen some Aatons with it, but even then it has always been described as "wildly unreliable"), so motion picture lenses are still usually marked in T-stops. Even though it isn't a turret anymore, the decision is still to mark then lenses in T-stops. Which I've grown more than used to, but it has always puzzled me to an extent: I've never seen a lens vary by more than a third of a stop from T-stop to F-stop. While knowing exactly how much light is transmitted is crucial, I don't see it as any more or less crucial than knowing what the depth of field is going to be. Near as I can figure, depth of field is so nebulous and contingent upon so many variables (from the subjectivity in what is considered to be out of focus to the variability in the size of an exhibition screen), that the lenses are marked in T-stops because the information derived from that is absolute.

Just a guess.

JeremyLangford · 03-12-2009

Quote:

Originally Posted by sevo

Almost right. The focal length is a constant, defined at infinity. The distance to the image plane however increases in proportion to the drecreasing distance to the object plane. At 1:1 magnification, a lens of 50mm focal length would have 100mm image and object distance each, with both side effects of going from 50 to 100mm - the increased coverage (image circle) a 100mm lens of a identical scaled design would have at infinity, and a corresponding narrower angle in relation to the constant image size.

Quote:

Originally Posted by Al Kaplan

...and at 1:1 you'd lose two stops of light reaching the film because of the law of inverse squares.

Wow that is getting confusing!^^^ Does anybody know of a book that could do a good job of explaining all of this kind of stuff me? The problem is that I learn extremely well with diagrams and pictures rather than text.

CCCPcamera · 03-12-2009

wow, it's nice to see a thread actually ABOUT cameras/lenses and not just about what lens to buy or which of one's several leicas to part with. Cool. I say grab a textbook, there's nothing better than a good textbook, no matter the subject. Check out a university library, that's where I'd look.

Al Kaplan · 03-12-2009

Jeremy, here we are in this 21st century world of computers, the internet, and Google? Just Google "law of inverse squares" and you'll find explanations, diagrams, drawings, everything that you ever wanted to know. Or just have FAITH that I'm a square shooter and not just jerkin' your chain.

JeremyLangford · 03-12-2009

Quote:

Originally Posted by Al Kaplan

Jeremy, here we are in this 21st century world of computers, the internet, and Google? Just Google "law of inverse squares" and you'll find explanations, diagrams, drawings, everything that you ever wanted to know. Or just have FAITH that I'm a square shooter and not just jerkin' your chain.

Yeah, you're right. After looking for a while, I found this wikipedia page with lots of good stuff thats been disussed in this thread.

http://en.wikipedia.org/wiki/Photographic_lens_design

Isn't it weird when a 17 year old is told by a 66 year old to use Google on a forum? My grandfather is turning 66 this year and he is completely oblivious to the wonders of the internet. I grew up right in the middle of Myspace and Facebook and so I'm on my computer a LOT! Without the internet, there's a high chance I wouldn't even be into photography. Anyways, just glad to see a lot of older people here that know the internet just as much as I do.