View Full Version : What makes a lens's focal length?
JeremyLangford
03-09-2009, 15:39
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?
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, 15:52
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.
http://farm4.static.flickr.com/3401/3248139239_79d76422c4.jpg
http://farm4.static.flickr.com/3510/3293408359_9c4b566d4d_o.jpg
http://farm4.static.flickr.com/3420/3281547952_260826b6dc_o.jpg
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, 17:09
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, 17:40
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, 00:42
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, 00:49
Roger: I understand this stuff already, and that is the clearest I have ever seen it explained.
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, 01:54
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, 02:00
. . . 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
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, 05:59
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.
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. :D
Al Kaplan
03-10-2009, 06:28
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, 06:43
Roger probably copied that from a book he already wrote. :D
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, 06:46
Damn, Brian, that Astignar is wild. I love it.
Al Kaplan
03-10-2009, 07:05
The scissors analogy is brilliant, Roger!
Roger Hicks
03-10-2009, 08:31
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.
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, 09:58
...and at 1:1 you'd lose two stops of light reaching the film because of the law of inverse squares.
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, 16:23
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.
...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, 16:48
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, 17:19
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, 18:14
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.
Al Kaplan
03-12-2009, 19:07
Jeremy, it might be weird indeed! I was thinking the same thing as I typed it, but then I'm weird. My ex, now a medical doctor, was a computer geek before Steve Jobs planted his first Apple seed. We had chads all over the house (Google "chad" if you need to) and she could write programs in both fortran and cobal by the early seventies. She also preferred doing calculations with a Chinese abacus, flicking beads with her pencil. She'd prove to anyone who doubted her that it was faster than an electronic calculator. Her dad was a nuclear physicist. Brainy women are cool, and don't write off crazy ol' dudes like myself. It's been an interesting life, and it ain't over with yet, even though "young chicks" now includes women over fifty. http://thepriceofsilver.blogspot.com
JeremyLangford
03-15-2009, 18:01
When it comes to a single element, double convex, spherical lens such as a magnifying glass, would the curvature of the glass element match the curvature of the angle of view curves showed on this picture? In other words, would a 28mm single element, double convex, spherical lens's glass element curvature match up with the angle of view curvature of 75 degrees shown in this diagram?
http://www.danmassey.co.uk/city&guilds_files/image020.jpg
Chris101
03-15-2009, 19:42
No. It is more complicated than that. The angle of view is a function of, not only the focal length, but of the size of the film (or image sensor) as well.
Chris101
03-15-2009, 20:01
When looking at the angle involved, it may help to look at a lens as a glorified pinhole. Here is the relationship between a pinhole approximating lens and its angle of view:
http://homepage.mac.com/cheilman1/images/cameras/pinholediagram.gif
JeremyLangford
03-15-2009, 20:13
When looking at the angle involved, it may help to look at a lens as a glorified pinhole. Here is the relationship between a pinhole approximating lens and its angle of view:
http://homepage.mac.com/cheilman1/images/cameras/pinholediagram.gif
So when the film plane is moved closer to the pinhole, the angle of view becomes wider right? Why is this?
Al Kaplan
03-15-2009, 20:29
Think of it as a rangefinder, Jeremy. If you know the angles of two corners of a triangle you can calculate the angle of the third corner, and with that combined information tell how far away they are from one another. Or if you know how far away, you find the angles. You can check it out in any basic geometry book, or you can just have faith that we're not trying to lead you down the wrong path. (...or maybe we are!) Nah! No full moon tonight.
JeremyLangford
03-15-2009, 20:48
Think of it as a rangefinder, Jeremy. If you know the angles of two corners of a triangle you can calculate the angle of the third corner, and with that combined information tell how far away they are from one another. Or if you know how far away, you find the angles. You can check it out in any basic geometry book, or you can just have faith that we're not trying to lead you down the wrong path. (...or maybe we are!) Nah! No full moon tonight.
I always trust everyone on this forum. But for some reason, I can't grasp the basics of photographic lens optics. I guess the best place for me to start is a pinhole lens. I understand that everything is in focus because the circle of confusion is so tiny. But I don't understand why the angle of view becomes wider when you move the pinhole closer to the film plane.
Chris101
03-15-2009, 21:08
Light travels in a straight line. Look again at the diagram I drew. The blue lines are two rays of light from the extremes of the field of view. They go straight through the pinhole onto the film, and hit it at the edge. Move the pinhole closer, and the angle increases, further and it decreases. All because the lines go straight from the object to the film, but must all go through the same point, the hole itself.
Here is the same diagram, but I've squished it, so that the focal length is shorter. Note that the angle is wider:
http://homepage.mac.com/cheilman1/images/cameras/pinholediagramshort.gif
It would be better if I had an interactive animated pinhole, where you could slide it up and down, and see how the blue lines expand and contract, but I don't.
Chris101
03-15-2009, 21:10
By the way, fisheyes are a special case. Their stated focal length is only applicable in the center of the lens. So don't include them in this 'pinholey' explanation.
JeremyLangford
03-16-2009, 09:13
I tried to add on to your diagram to help myself understand. Does this look right?
http://img394.imageshack.us/img394/1651/dia.jpg
If so, then it seems like having a longer focal length will require longer exposures because of all of that light that is being sent out past the sides of the film plane. Is that true?
When it comes to a single element, double convex, spherical lens such as a magnifying glass, would the curvature of the glass element match the curvature of the angle of view curves showed on this picture? In other words, would a 28mm single element, double convex, spherical lens's glass element curvature match up with the angle of view curvature of 75 degrees shown in this diagram?
One answer in addition to Chris' comments:
Two things determine how a light ray is bent (refracted) when traversing glass: the angle of incidence (the curvature of your double convex element), and the refraction indices of the two materials on each side of the surface (glass and air). There are different glass types with different indices. So, for a given focal length, different curvatures are needed depending on index.
See also here:
http://en.wikipedia.org/wiki/Refraction
Best,
Roland.
JeremyLangford
03-16-2009, 09:45
One answer in addition to Chris' comments:
Two things determine how a light ray is bent (refracted) when traversing glass: the angle of incidence (the curvature of your double convex element), and the refraction indices of the two materials on each side of the surface (glass and air). There are different glass types with different indices. So, for a given focal length, different curvatures are needed depending on index.
See also here:
http://en.wikipedia.org/wiki/Refraction
Best,
Roland.
So basically, a single element lens can look different than another single element lens with the same focal length if they have different types of glass?
Roger Hicks
03-16-2009, 09:46
So basically, a single element lens can look different than another single element lens with the same focal length if they have different types of glass?
Dear Jeremy,
Yup.
Cheers,
R.
Chris101
03-16-2009, 11:02
Like Roger said, yep, (er, yup) that is why you hear things like ED glass. It means the 'special' glass has a different index of refraction (the amount the glass bends light.)
Your diagram is correct. More light hits the film with a shorter distance between the pinhole and the film. As light travels from a source (in this case, the pinhole) it spreads out. And as it spreads, any one point becomes dimmer. If light can spread unrestricted, then it gets dimmer as the square of the distance. That is twice the distance makes it 4 times dimmer, and 3 times further is 9 times dimmer. Now to move from the pinhole to a lens:
A lens improves on a pinhole, because the light from it's entire surface is bent toward the film. The f-number of the lens's opening is relative. A long lens has a larger opening than a short one with the same f-number, so the amount of light hitting the film is the same. A pinhole would become terribly blurry if a large aperture were used. Pinholes become unusable larger than about f/128.
JeremyLangford
03-16-2009, 11:24
Like Roger said, yep, (er, yup) that is why you hear things like ED glass. It means the 'special' glass has a different index of refraction (the amount the glass bends light.)
Your diagram is correct. More light hits the film with a shorter distance between the pinhole and the film. As light travels from a source (in this case, the pinhole) it spreads out. And as it spreads, any one point becomes dimmer. If light can spread unrestricted, then it gets dimmer as the square of the distance. That is twice the distance makes it 4 times dimmer, and 3 times further is 9 times dimmer. Now to move from the pinhole to a lens:
A lens improves on a pinhole, because the light from it's entire surface is bent toward the film. The f-number of the lens's opening is relative. A long lens has a larger opening than a short one with the same f-number, so the amount of light hitting the film is the same. A pinhole would become terribly blurry if a large aperture were used. Pinholes become unusable larger than about f/128.
Ok, so a shorter focal length pinhole camera will recieve more light due to light's inverse-square law. But what about all the light that is not even hitting the film plane on the longer focal length of this diagram? Wouldn't that be another factor that makes longer focal lengths slower? How come that light doesn't bounce off the inside walls of the camera and fog the paper somehow?
http://img394.imageshack.us/img394/1651/dia.jpg
How come that light doesn't bounce off the inside walls of the camera and fog the paper somehow?
It does. That is why you paint the cameras insides black and create the surfaces to have light trapping properties where misdirected light is reflected towards a long chain of absorbing surfaces rather than towards the film.
Sevo
Roger Hicks
03-16-2009, 11:47
It does. That is why you paint the cameras insides black and create the surfaces to have light trapping properties where misdirected light is reflected towards a long chain of absorbing surfaces rather than towards the film.
Sevo
(For Jeremy, obviously, not you)
It's also why flare factors vary from close to unity to 4 or more.
The flare factor is the difference between the brightness range of the original scene and the brightness range of the focused image, where the darkest areas have been 'filled' by all the stray light bouncing around.
Scene brightness range 1000:1, image brightness range 800:1, flare factor 1.25. Image brightness range 500:1, flare factor 2. Image brightness range 250:1, flare factor 4.
This is why some lenses (and cameras) are contrastier than others.
Tashi Delek,
R.
JeremyLangford
03-16-2009, 12:04
It does. That is why you paint the cameras insides black and create the surfaces to have light trapping properties where misdirected light is reflected towards a long chain of absorbing surfaces rather than towards the film.
Sevo
Oh yea, that makes sense.
HankOsaurus
03-17-2009, 09:48
Greetings, Forum.
Jeremy, I'm almost 62 and I am learning from the talented and knowledgeable folks contributing to this thread as you are ... even though I have been using manual cameras since the mid 60's. Thanks for asking the questions that spawned this excellent discussion.
Chris, you set me to thinking about pinhole cameras, diffraction, and effective aperture.
I read a year or so ago that someone set out to make the world's largest pinhole camera. If I recall correctly, it was an airplane hangar! I wonder what the diameter of the "pinhole" was, and what its effective aperture was at the distance of the width of an airplane hangar. I would guess that it would work out to a pretty big F number, counting the pinhole diameters it would take to get across that hangar to the opposing wall.
Happy day.
HankOsaurus
03-21-2009, 05:21
Hi Folks.
Just found a link with some technical details about that big pinhole camera I mentioned upthread:
http://news.softpedia.com/news/The-World-039-s-Largest-Camera-and-Photograph-62423.shtml
According to the link, the aperture of the pinhole was 6mm. The distance from it to the back wall of the hangar was 79 feet, six inches. That translates to 24,231.6 mm. Divided by 6 mm, that comes out to an F number of 4,038.6 !
Chris101
03-24-2009, 19:33
Dang Hank.
I used to live in El Toro in the '60's. And I just spent the last week in that area. Had I the foresight to check RFF before going on vacation, I could have made this hangar a destination! Talk about past/present/future!
Thanks for that link. The problem with cameras that big is that you can basically only take one picture! Oh, and I'd crop it.
Jeremy- a really fun way for you to begin to get a handle on this would be to turn your room in to a camera obscura. If you aren't familiar with a camera obscura, check out the wikipedia article (there is also a really good indie folk/pop band sort of akin to belle and sebastian of the same name). All you will need is some opaque black plastic sheeting from lowes or home depot, a knife, and a roll of actual honest to goodness gaffer tape (blue painters tape *might* work in a pinch, you just need a tape that isnt going to remove paint or wallpaper or leave a residue behind). tape up the cracks around your door, and cover your window or windows with the black plastic sheeting. Get the room to the point where it is so dark, even at midday, that you can't perceive your hand right in front of your face when you wave it about. Then, cut a small round hole in the plastic sheeting over a window and watch as the image of whatever is outside your window appears on the opposite wall, upside down and backwards.
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