Aperture and F-stops

[Helen B]

Whatever it means is totally unimportant.
Work on ideas and communicating the passion and pleasure you feel for images.
Have fun.

I'm all for having fun. I won't, however, presume to know what is important to other people but I am happy to try to satisfy someone's genuine curiosity. Fortunately there's no need to fear that understanding things like this will diminish one's creative side. Understanding and creativity/vision are not in a zero-sum competition.

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There are a few ways of arriving at f/0.5 as the theoretical limit for a photographic lens. Perhaps the easiest to visualize comes from the requirement that the rear (also called the second) nodal plane of the lens must be a spherical cap (a part of the surface of a sphere) if coma (a major lens defect) is to be corrected for. Correcting for coma does not mean eliminating it, by the way.

On the optical axis of the lens, the rear nodal point (where the axis intersects the rear nodal plane) is one focal length away from the image plane, for an object at infinity - so you can imagine the nodal plane as being on a sphere whose radius is the focal length of the lens. Clearly, the nodal plane cannot subtend an angle of more than 180 degrees from a point on the image plane - the largest it can be is a hemisphere.

Now, the use of the diameter of the entrance pupil to calculate f-number is only an approximation, albeit a fairly good one, and one that is accepted by the ISO as a photographic definition. It is more correct to use the angle subtended by the illuminated part of the nodal plane, and to use the formula f-number = 1/(2 * sin theta) where theta is the half angle. As that half angle can never exceed 90 degrees (and as the sin of an angle can never exceed 1), the smallest f-number is 0.5. One might be tempted to use tan theta in the formula, which would allow the f-number to approach zero in theory, but sin theta is correct because of the requirement for the rear nodal plane to be a spherical cap.

It is also possible to use the second law of thermodynamics to arrive at the same result (ie that a passive system cannot produce an image that is brighter than one produced by an f/0.5 lens).

(I've made a few simplifications here to try to avoid an overly contorted and tedious answer)http://www.quora.com/Camera-Lenses/How-are-ƒ-1-0-lenses-possible#

Ask if anything is unclear.

Best,
Helen

 

[KmH]

Thanks Helen!

I love the technical stuff!

 

[Christer]

AAh, I had to read through it a few times, but I understood it in the end
But why does theta = 1/2*(angle) ?

 

[Helen B]

If I understand your question correctly, the half angle is used instead of the full angle so that a right-angle triangle is being considered. This makes the trigonometry much easier. Does that answer your question? If I had time I would draw some diagrams.

Best,
Helen

 

[Christer]

Oh, yeah that does make sens. It would be more difficult to measure the angles if you don't have a right angle.You don't need to draw any diagrams on my behalf.
Thanks for the information

 

[table1349]

This maybe a stupid question... But I'm going to ask it anyway...

I recently bought the D7000 camera that comes with the 18-105mm lense. On the camera box, it sepcifies the lense "AF-S DX NIKKOR 18-105MM f/3,5-5,6G ED VR".

I took my camera out on a sunny day, set it to aperture priority to test how many f-stops my lens was capable of, it goes from 3,5 - 22... So my question is, what does f/3,5-5,6G mean?

Good resource for understanding such thing: Digital Photography Tutorials