Why is aperture a ratio?

[Turnerea]

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....

 

[Ls3D]

Now toss in the crop factor for your camera body and,... I try not to think about it too much, but it is an interesting question - I'll check back and see how this one plays out.

-Shea

 

[tirediron]

Don't forget to factor in the focal length. Let's assume a 50mm lens set at f10; this has an aperture of 5mm. A 25mm lens at f10 would have an aperture of 2.5mm...

 

[Josh66]

Don't forget to factor in the focal length. Let's assume a 50mm lens set at f10; this has an aperture of 5mm. A 25mm lens at f10 would have an aperture of 2.5mm...

The question he's asking is (using the numbers in your example): Why does an opening of 2.5mm in a 25mm lens let in the same amount of light as the larger opening of 5mm in the 50mm lens?

I know they do let in the same amount of light, but I forget why...

 

[DeadEye]

The physics of light. If it were not done in ratio it would be very hard to determine correct exposure.

Helen could explain it best.

 

[Turnerea]

The question he's asking is (using the numbers in your example): Why does an opening of 2.5mm in a 25mm lens let in the same amount of light as the larger opening of 5mm in the 50mm lens?

I know they do let in the same amount of light, but I forget why...

Yes... that is my question. Though now that I'm thinking about it more, it is making *some* sense, even though I can't quantify it.

Does it fundamentally have to do with the fact that because the two different sized apertures (2.5mm and 5mm in the example above) are at different lengths from the image plane they in effect let through the same amount of light. I'm sort of visualizing two cones... one cuts off the cone near the tip (sensor) and is smaller, while the one further away form the sensor is bigger... but because they're on the same conical surface, they're letting through the same amount of light?

 

[DeadEye]

The more you magnify an object the more light loss there is. I could be wrong so hopefully helen will chime in later.

 

[Dao]

That's what I think. I could be wrong.

Example:
Same sun, when the sun ray hitting the equator, it is hotter or brighter than the sun ray hitting other regions. It's because of the light density are different (angle of sun ray hitting the earth surface are different)

The angle of views are different from different focal length lens. Smaller the focal length yield a wider angle of view, hence more lights are converged and hitting the sensor . When you compare to a longer focal length (assuming same front lens diameter), smaller angle of view and less lights are converged and hitting the same sensor.

Since the density of light are different, so the actual physical diameter of the aperture should be different.

 

[Josh66]

That's what I think. I could be wrong.

Example:
Same sun, when the sun ray hitting the equator, it is hotter or brighter than the sun ray hitting other regions. It's because of the light density are different (angle of sun ray hitting the earth surface are different)

The angle of views are different from different focal length lens. Smaller the focal length yield a wider angle of view, hence more lights are converged and hitting the sensor . When you compare to a longer focal length (assuming same front lens diameter), smaller angle of view and less lights are converged and hitting the same sensor. So the density of light are different

So basically the intensity of the light is reduced due to the narrow field of view - is that what you're saying? Seems to make sense...

 

[Dao]

Basically, that is what I mean.

 

[epp_b]

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??

Yes, you've basically got it. The only piece of the puzzle that you're missing is the relation between light and focal length

Now toss in the crop factor for your camera body and,... I try not to think about it too much, but it is an interesting question - I'll check back and see how this one plays out.

Crop factor has nothing to do with how much light is let into a lens. It only affects the field of view.

The simple answer as to why it is expressed as a fraction and not an absolute number is because the same fraction is a different absolute number for each focal length, but it expresses the same amount of light regardless of focal length.

A 400mm f/2.8 lets in the same amount of light as a 18mm f/2.8, even though the diameter the aperture is ~143mm and ~6mm respectively.

f/1.8 for 50mm is a ~28mm opening, but it's a ~22mm opening for a 40mm length, ~19mm for 35mm, and so on and so forth. Imagine having to calculate the aperture diameter in millimeters for each focal length

So basically the intensity of the light is reduced due to the narrow field of view - is that what you're saying? Seems to make sense...

The light isn't less intense for longer focal lengths, there's just less of it.

 

[tirediron]

The question he's asking is (using the numbers in your example): Why does an opening of 2.5mm in a 25mm lens let in the same amount of light as the larger opening of 5mm in the 50mm lens?

I know they do let in the same amount of light, but I forget why...

Because:

Don't forget to factor in the focal length

Isn't that pretty much exactly what epp_b said in his post using the paper tube analogy?

 

[epp_b]

Isn't that pretty much exactly what epp_b said in his post using the paper tube analogy?

Yes, even though I deleted it and thought of a better way to describe it

 

[tirediron]

Yes, even though I deleted it and thought of a better way to describe it

Oh sure, go all Helen on us why don't you? :greenpbl:

 

[epp_b]

Uhm...I don't think I've been here long enough to know what that means