[Soupdragon]

I wrote this on another forum so, for the benefit of those who did not already know (which is probably nobody) here is my explanation of the f-stop.

**Feel free to flame me if this is wrong**

The f-stop is the relationship between the focal length of your lens and the hole size formed by the aperture blades.
For example:

A 50mm lens at f1.0 has an aperture hole of 50mm dia (50 divided by 1)
The same lens at f2.0 has an aperture hole of 25mm dia (50 divided by 2)
The next whole f-stop is f4.0 and has an aperture size of 12.5mm dia (50 divided by 4), which at first may seem a bit strange until you realise these are octave spacings (doubling each time).
The reason for this can be understood if you calculate the area of the circle made by the aperture at any given stop by using the following, and the fact that light and for that matter sound, obey the four square law.

50mm lens @ f2.0
50mm divided by 2 = 25mm which equals the diameter of the hole.
Divide the diameter of the hole by 2 to give you the radius, 25mm divided by 2 = 12.5mm.
Square the radius then times it by pi, 12.5mm times 12.5mm then times 3.141 "ish"
should give you about 491 or 491 square mm, the surface area of the hole.

"So what happened to f1.4 and the likes?" I hear you say.

These can be derived from doing effectively the reverse of calculating the surface area.

So to calculate a half stop we can do the following:

At f1.0 the area of the aperture is 1963mm so, if we half that to get half a stop we get 981.5mm squared.
Divide that by pi (3.141) we get 312mm ish.
Take the square root of 312 and we get 17.6mm ish (the radius).
Double that to get diameter 35.5mm ish.
Divide the lens focal length of 50mm by the aperture diameter of 35.5 and we get, (drum rolllllllll), 1.4 or f1.4.

**********I was going to include a table of all f-stops and their relationships with each other but could not get the spacing format right***********.

[fionaB]

ok... as some ( who shall remain nameless) already know............ sometimes im a bit slow on the uptake...... especially if it concerns numbers......... so i read the first few lines and i knew i had to stop....... it probably makes perfect sense...... but the minute i read divide........... i ran.........
thanx for posting it soup I will leave it to the more numeric people to read it all and perhaps one day when i get over my fear of numbers i will read AND understand!

[Soupdragon]

I really just wanted to help people understand where numbers like f1.8 and f5.6 came from.
I obviously didn't do a very good job, sorry.

[Soupdragon]

I was going to wrire a thread on DOF calculations but given what you just said, it will be difficult to get people to read the thread let alone do the math.
Ho Hum.

[fionaB]

soup...... no it was great I was meaning its me! grrr thats the down side about type you cant inflect in words what vocals do! Soup seriously it is a great article and not for one moment did i mean it otherwise, i was just saying that i cant do numbers! sooooo sorry if you thought i meant it in any other way!

[Soupdragon]

No I did not mis-understand what you were saying I just wish I had put it over in a way that would make you want to reach for a calculator and have a go.
I know with modern cameras you don't really need to know these things, I just thought people might be interested.

[fionaB]

I amsure they will be interested Soup..... i am absolutely hopeless at it tho... ask Rob, he spent hours trying to teahc me the inverse square rule thingy before the penny finally dropped....... numbers terrify me and the last thing i wanted to do was to put people off reading it. wish i had just not replied now. perhaps the crew can remove the reply?

again u have my deepest apologies!

fiona

[lolyton]

I take it from that the Scheimpflug principle essay i'd planned will not be needed.

People don't necessarily need to understand these principals with new instant digital cameras, but it goes a long way to helping peoples understanding of what they are doing and will in the long run give people more control over exposures and DOF and quicker handling of the camera if they have a reasonable understanding of the above. Which in my view can only be a good thing and always worth a try to teach people new things.

I am only joking about my Scheimpflug principle essay, however it is something i have studied (many boring weeks of it trying to learn it without needing the formula written down) and it had vastly improved my handling of bellows cameras e.g.5x4. However it is now long forgotten.

[Steve]

Originally Posted by Soupdragon

**********I was going to include a table of all f-stops and their relationships with each other but could not get the spacing format right***********.

First of all thanks for writing this out and with your permission I will convert and display it as one of our articles on the pixalo main site.

With regard to the layout of the table try placing it in [code] tags as that usually will help with the alignment. Even if thats not possible if you are happy with me displaying this as an article please forward it (with table) to my email addy. steve @ pixalo.com

Originally Posted by lolyton

I take it from that the Scheimpflug principle essay i'd planned will not be needed.

Same as above Lolyton, if you want to write and provide the article I will gladly format it and display it in our articles section. You will retain full credit for your work and obviously will recieve reputation points as a thank you.

[Soupdragon]

I'll get on with generating the table this evening.
It will be in excel format, how do I upload it (I'm just not too hot with computers).

Feel free to re-format it or edit it in any way you see fit, I require no credit for it, it's just I thought someone might like to know.
I tried searching for other articles of this ilk here but could not find anything.
I might give the DOF calculations a miss as it is rather hard to describe without graphics.
Unless of course I start with perhaps the circle of confusion.

[Soupdragon]

f/stop Diameter of aperture (mm) Radius of aperture (mm) Area of aperture (sq. mm) f/1.050251,963f/1.435.717.91,002f/2.02512.5491f/2.817.98.9250f/412.56.3123f/5.68.94.563f/86.33.131f/114.52.316f/163.11.68f/222.31.14f/321.50.82

[Steve]

Originally Posted by Soupdragon

I'll get on with generating the table this evening.
It will be in excel format, how do I upload it (I'm just not too hot with computers).

from my post above

Originally Posted by Steve

With regard to the layout of the table try placing it in [code] tags as that usually will help with the alignment. Even if thats not possible if you are happy with me displaying this as an article please forward it (with table) to my email addy. steve @ pixalo.com

[Soupdragon]

Hmmmm! does computer illiterate spring to mind?
The data is there it just wants re-arranging, a bit, and the use of your imagination.

Do I need to put the spaces into your mail address because it did not work?

[Steve]

No leave out the spaces from my email addy...I placed them in to break the link and reduce potential spam