[FarmerJim]

Why can two lenses of the same focal length and same aperture have vastly different dimensions?

If I look at the Pentax 50mm f1.4 lens, I see a small objective lens/front element.
If I look as the Sigma 50mm f1.4 lens, I see a large objective lens/front element.

The Pentax lens has a 49mm filter thread, the Sigma a 77mm, yet both are full frame 50mm f1.4 lenses. Just looking at the lens housing, it seems like the Sigma will let more light in. The Sigma is about a third wider and twice as long as the Pentax.

I know that there is probably a formula/rule that calculates the aperture based on some measurements... can somebody explain it to me?

Thank you.

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Last edited by FarmerJim; 05-17-2016 at 12:28 PM. Reason: Typo correction

[mattb123]

I think it mostly just comes down to different optical formulas and coatings. The formulas are usually expressed as "x elements in y groups" and depending on how that is set it may let more or less light in that would need to be compensated for with a bigger diameter. Coatings will affect this too with some transmitting more light than others.

Kind of like how there can be two different 2.0L 4 cylinder engines with different outputs and economy depending on their designs.

[jatrax]

I know that their is probably a formula/rule that calculates the aperture based on some measurements... can somebody explain it to me?

I do not think it is just a simple formula. The number of elements, air gaps, type of glass, coatings and probably some other stuff all need to be factored in. The more elements, and the more the designer tries to correct for optical aberrations the bigger the lens needs to be to deliver the same amount of light to the sensor. The older film era lenses were often very small because of the simple designs. Modern lenses are becoming more complex and larger.

Also, Sigma seems to design without much regard to size or weight, but Pentax has traditionally included size and weight as a design criteria.

[jeverettfine]

A lens aperture is an exact measured ratio of the diameter of the diaphragm to the focal length of the lens. A 50mm lens with a 25mm opening will be f/2.0. 35.7mm opening would be f/1.4. The Sigma 50mm f/1.4 and the Pentax 50mm f/1.4 have exactly the same aperture size. The exact dimensions of the front element, rear element, length of lens etc is determined by the lens design...two elements, three, six, an aspherical one, etc etc. Search "Lens (optics)" and you will find some pretty detailed explanations.

[Ontarian50]

There's a whole hornet's nest of optical issues when bringing up lens formulas.

Basically, the simple formula has it that the lens' physical aperture diameter is divided into the focal length. So a 25mm wide aperture in a 50mm lens makes it an f2.0. A 50mm 1.4 lens would have a 35.7mm diameter aperture.

A super simple two-element lens might have elements barely bigger than that 35.7mm diameter, and be physically tiny - but it would be optically crappy.

Here's a photo of four lenses, taken from the back side. Can you tell which ones are 50mm 1.4's?

Well, of course, they all are. The little one is the very first 50mm 1.4 - the Nikon 5cm 1.4 for the rangefinder camera. Based on a Sonnar design, it is quite compact. SLR camera designers had to go to the more complex Gauss and Double Gauss designs to make a lens just as bright that would clear the moving mirror. If you keep adding lens elements to improve optical performance, then things just keep getting bigger - mainly up front, because there's no room at the back, so close to that mirror.

A really interesting lens is the 58mm Topcor. The old Topcon RE used the tiny Exacta type mount, so the resulting lens had a narrow "waist" at the mount, but a huge front element.

[FarmerJim]

Related question then... If the aperture is 1.4 on a 50mm lens, the lens has a 37.5mm aperture diameter. Wouldn't a larger lens, like the Sigma in my example, let more light in just because of the increased surface area of the lens?

Can there be that much light loss going from a large element with a 77mm filter size, and very little light loss when compared to a small front element with a 49mm filter size to the same 37.5mm aperture opening?

[stevebrot]

If the aperture is 1.4 on a 50mm lens, the lens has a 37.5mm aperture diameter.

The lens diameter is not the aperture diameter, nor is such always the size of the iris opening, per se. The f-number is the ratio of focal length:entrance pupil diameter when focused at infinity and that diameter may or may not correspond to the size of the physical iris opening and is not bound directly by element size.

Wouldn't a larger lens, like the Sigma in my example, let more light in just because of the increased surface area of the lens?

Good question. The simple answer is that flux within the frame is the same. Going further, two lenses with the same image circle and relative aperture (f-number) will have the same amount of light to the image plane regardless of front element diameter or focal length or format! No light lost, no light thrown away.

Going back to the simple case of same format, same focal length, same aperture, different size front element. The answer becomes clear when you trace the rays at frame edge and realize that the "view" from the image plane is the same. You can't take in more light than what is coming from the subject...or at least it is not a good thing to do so. When we do, it is called "flare".


Steve

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Last edited by stevebrot; 05-17-2016 at 01:13 PM.

[stevebrot]

There's a whole hornet's nest of optical issues when bringing up lens formulas.

Basically, the simple formula has it that the lens' physical aperture diameter is divided into the focal length. So a 25mm wide aperture in a 50mm lens makes it an f2.0. A 50mm 1.4 lens would have a 35.7mm diameter aperture.

A super simple two-element lens might have elements barely bigger than that 35.7mm diameter, and be physically tiny - but it would be optically crappy.

Here's a photo of four lenses, taken from the back side. Can you tell which ones are 50mm 1.4's?

Well, of course, they all are. The little one is the very first 50mm 1.4 - the Nikon 5cm 1.4 for the rangefinder camera. Based on a Sonnar design, it is quite compact. SLR camera designers had to go to the more complex Gauss and Double Gauss designs to make a lens just as bright that would clear the moving mirror. If you keep adding lens elements to improve optical performance, then things just keep getting bigger - mainly up front, because there's no room at the back, so close to that mirror.

A really interesting lens is the 58mm Topcor. The old Topcon RE used the tiny Exacta type mount, so the resulting lens had a narrow "waist" at the mount, but a huge front element.

Love it when people throw a rangefinder lens into the mix. Thanks too for mentioning the Topcon.


Steve

[FarmerJim]

http://optdesign.narod.ru/book/Handbook_of_Optical_Design.pdf

In particular, pay attention to chapters 1-3, 8, 11, and 12, and you might begin to understand the design differences in these lenses.

Thank you for the link, that looks like what I need to answer my question.


Thanks to all who provided responses here.

[Na Horuk]

Here is how I understand things, and hopefully someone will correct me or tell me I'm right.
First, there is F-stop (aperture) and T-stop (transmission). The difference is that T is the actual brightness that gets through - it depends on the F, but it not the same. Why? Because glass, the materials, lens coatings, things like that cause a loss of light. And different lenses have a different amount of light lost - so some lenses are a little darker than others at a given aperture.
Aperture is the next term, which is a fraction of the opening and focal length. But the aperture is between the aperture blades, not just the front element radius. With old style, relatively simple lenses, this difference was not very big. But with modern glass, they can pack in a lot of corrections in front of the aperture, which causes the front of the lens to be huge (this can particularly be seen with Sigma Art series, but also some modern Zeiss lenses). But even if you shoot wide open, at maximum aperture, there is still a smaller aperture than the front of the lens. Its a cone, not a tube.

[MJSfoto1956]

the best way to make a lens small is to get the rear element to be as close to the sensor as possible. Newer lens designs can take advantage of this in ways that film-era lens designers couldn't fathom. To wit: the DxO One lens is amazingly small (even for a 1" sensor) but is f/1.8:



<prediction> as we near the end stages of sensor improvement (it is already plateauing somewhat) I would imagine that lenses will incorporate the sensor built into them -- and the camera "body" to which it attaches will be merely for controls and storage. The DxO One is but a preview of that: the iPhone acts like the body while the DxO One is (mostly) just the lens. But such a paradigm shift won't come from any existing camera manufacturer: they have too much invested in the current paradigm. Perhaps a lens manufacturer like Samyang or similar might be daring enough to buck the trend.</prediction>

Michael

[stevebrot]

http://optdesign.narod.ru/book/Handbook_of_Optical_Design.pdf

In particular, pay attention to chapters 1-3, 8, 11, and 12, and you might begin to understand the design differences in these lenses.

Thanks for providing that link. Good references for optical theory are hard to come by on the Web and this one has now been added to my reference library. There is an additional site that I have found useful and which is rather strange due to its purpose. Mark Goodman's coinimaging.com site caters to people who do macro photography of collectable coins. Part of the content is one of the coolest collection of "simple" optical reference articles that I am aware of. Although the articles are intended to be read in order, I usually pick the article I am interested in and reference back if I see something unfamiliar.

http://coinimaging.com/photo_articles.html (May load slowly at times)

All in all, Goodman covers many of the more sticky questions in a very concise manner and while he sometimes misses, overall I have found his work valuable. What amazed me was the revelation that doing good macro work in a predictable manner requires a fairly complete understanding of how lenses and optical systems work.


Steve

[FarmerJim]

Here is how I understand things, and hopefully someone will correct me or tell me I'm right.
First, there is F-stop (aperture) and T-stop (transmission). The difference is that T is the actual brightness that gets through - it depends on the F, but it not the same. Why? Because glass, the materials, lens coatings, things like that cause a loss of light. And different lenses have a different amount of light lost - so some lenses are a little darker than others at a given aperture.

I think this is what I was thinking of. T-stop

The calculated f-stop would be the same, but the lens design might let more or less light through the aperture opening. T-stop.

So the aperture is the size of the opening and the ratio of light going through it, doubling/halving of the light by aperture steps.
The T value (I don't know the term yet) is the amount of light going through that opening.

So we can have two lenses, both 1.4 with different amount of light passing through them. Correct?

(I just searched for this and found info here via Google)

[BigMackCam]

http://optdesign.narod.ru/book/Handbook_of_Optical_Design.pdf

In particular, pay attention to chapters 1-3, 8, 11, and 12, and you might begin to understand the design differences in these lenses.

Thanks for that link... It all makes sense now!