Aperture and “Stops” – Mathematicized


Even before I bought my first DSLR, I had a theoretical understanding of “Aperture”. I knew that aperture represents the small opening at the back of the lens, which controls the amount of light passing through the lens and hitting the sensor. I also knew that an aperture of 2.8 allows double the amount of light than an aperture of 4. I recognized these numbers in the table below, and also understood that any F-number allows double the amount of light than the immediate next F-number on its right.

f-stop 2 2.8 4 5.6 8 11 16 22 32 45

 

However, I was never able to understand the reasons behind these specific values used. These numbers, 2.8, 5.6, 11 were like accounting principles. If you don’t know me well, lets just say accounting and I are like acquaintances that are better off as acquaintances. When accounting and I meet, we just press our lips together tight, reverse nod with raised eyebrows, and keep walking our way.

If you want to explain a concept to an Indian, explain the math behind it. Once I understood the math behind those “F-stops”, those numbers started making sense. It was actually so ridiculously simple, that I will soon come across as an idiot who couldn’t figure a “Level: Noob” concept out for so long.

So what is an f-stop number?

So, here goes. For now, lets assume that we are looking at a 50mm lens

  1. F-Stop numbers are actually reciprocals of the focal length – which means 2.8, 4, 5.6 etc are actually 50/2.8, 50/4, and 50/5.6 etc respectively
  2. This above F-Stop number represents the diameter of that opening behind the lens – simple!

Lets move ahead with the maths and make things more clear. Next, using these diameter values, we will compute the area of a opening behind the lens. Area of a circle is computed as pi x radius square = (22/7) x (diameter/2)^2

f-stop 2 2.8 4 5.6 8 11 16 22 32 45
area 7857.14 4008.75 1964.29 1002.19 491.07 259.74 122.77 64.94 30.69 15.52

 

This means that a 50mm lens, at an aperture of f/2 will have an area of 7857.14 (mm square ofcourse). This is roughly twice the area at an aperture of f/2.8 (which is 4008.75 mm square). In other words, at f/2, the lens opening is double in area as that of the opening at f/2.8, and so on. Now its easier to understand that at f/2, a lens will allow double the amount of light to pass through on to the sensor, than at f/2.8, and so on.

On an important side note, most DSLRs allow change in aperture in 1/3rd stops of light. Which means that if you wish to go from f/5.6 to f/8 or vice-versa (change in one whole stop of light), you will need to turn the aperture dial by 3 clicks.

What else can we take away from here?

Once the above understanding was established, the following started flowing automatically

  • Since the diameter of the lens opening is actually (focal length / f-stop), as the focal length of a lens increases, the overall diameter for the same f-stop also increases. Hence, an f/2.8 wide angle lens of say 18mm can be manufactured with a much more compact size, than a f/2.8 telephoto lens like 200mm. This is because, since at 200mm f/2.8 the opening will be wider. So, in order to maintain a sharp image, more lens elements have to be added and these lens elements have to be larger in size.
  • If we are talking about fixed aperture zoom lenses, like the 70-200mm f/2.8, a fixed aperture doesn’t mean that zooming the lens will not affect the aperture blades. Keeping the aperture fixed at f/2.8, when you zoom from 70mm to 200mm, the aperture blades will have to open up more to keep the aperture constant at f/2.8.
  • Since we also know that a large aperture yields a shallower depth of field, a 200mm f/2.8 will yield a shallower DOF than a 70mm f/2.8 will. This is because, as explained above, at 200mm f/2.8, the aperture blades have to open up more.
Aperture and "Stops" - Mathematicizedprag
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4 comments on "Aperture and “Stops” – Mathematicized"

  1. Pragalbh.. what a gem of a site, sooper cool! Is on my bookmark & am going to visit this space more often – keep it flowing!!

  2. Brilliant write up and so much knowledge simplified… keep posting. Cheers!!!

  3. I hit upon your website accidently. Great to know you switched to something passionate. From IT Consulting to Photographer is quite a shift.

    Good Luck !!

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