What makes a lens's focal length?

[Wiyum]

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]

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]

nice

nice

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]

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]

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]

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]

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?

 

[Chris101]

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]

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:

 

[JeremyLangford]

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:

So when the film plane is moved closer to the pinhole, the angle of view becomes wider right? Why is this?

 

[Al Kaplan]

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]

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]

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:

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]

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]

I tried to add on to your diagram to help myself understand. Does this look right?

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?

 

[ferider]

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]

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]

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]

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]

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?