Why is aperture a ratio?

[Josh66]

Apologies, you are correct - I did misunderstand. I read the relevant posts probably three times, and read them incorrectly all three times. Sorry for any confusion caused to the OP or anyone else. :blushing:

It happens...

I didn't quite know what to make of your comment (it's so hard to know what people are really saying online sometimes, no body language or inflection to go off of...). Sorry if my post (the "you talkin' ****?!" one) came off sounding combative, it wasn't meant to - but re-reading it, it feels that way.

Apology accepted.

 

[Tiberius47]

Imagine it as a wall with a hole in it. The hole will appear to be a certain size. As the wall moves further away, the hole appears smaller and smaller in your field of vision. to keep it the same apparent size, the actual size of the hole has to increase.

So if you have f4 on a 200 mm lens, the actual diameter of the aperture is much larger than f4 on a 50mm lens. However, the 50mm lens has a wider field of view and is thus collecting light from a wider angle. So to compensate for the 200mm lens collecting less light, the apertures have to be wider than the equivilent aperture on a shorter lens.

 

[Helen B]

This thread is an excellent example of the same thing being written in different ways. The individual contributors have not simply rewritten the preceding posts: they have written the answer in their own words, in the way that they understand the issue. This is surely not a purposeless bad habit, but a good, helpful one.

As can be seen in this thread, there are two approaches in general use: they could be called the 'constant angle' and the 'constant area ratio' approaches.

(Non-technically minded readers can stop reading now, if they wish!)

The simple relationship between f-number and the angle the aperture makes at the image plane is

N = 1 / (2 sine theta)

where N is the f-number and theta is half the angle subtended by the aperture at the image plane on the lens axis.

The maximum value the sine function can have is 1, therefore the minimum value the f-number can have is 0.5. This agrees with other methods of calculating the minimum possible f-number.

Best,
Helen

 

[mrcrassic]

I've read some of the beginning photo books, done a good amount of searching online- I understand all the basic concepts of aperture, shutter speed, ISO to get a proper exposure.

I'm just confused as to why aperture is expressed as a fraction. I understand how the stop system works to increase/decrease the area by 2, but for different focal lengths, I don't understand why the same f number corresponds to the same amount of light (assume the same shutter speed).

For Example
If you had f/1.8 on a 55mm lens, wouldn't that equate to more light into the sensor than f/1.8 on a 24mm lens? The actual diameter of the opening for the 55mm lens is 55/1.8=30.5mm, while for the 24mm lens it is 24/1.8=13.3mm, right? Now the area just scales linearly, so the areas are different... maybe I'm missing a concept here??

Hopefully that makes sense, and someone might have a suggestion for another way of thinking about it that might help myself and others who might have questions along the same lines....

Because aperture is a function of lens diameter and focal length.

f= N = f/D, f=focal length, D=lens diameter

Reference: http://en.wikipedia.org/wiki/F-stop

 

[Helen B]

Because aperture is a function of lens diameter and focal length.

f= N = f/D, f=focal length, D=lens diameter

Reference: http://en.wikipedia.org/wiki/F-stop

I think that the OP knew that. The question was 'Why?'

Best,
Helen