Wednesday, June 9, 2010

About f/stops and Apertures

When I saw the AdoramaTV video regarding the f/stop of a lens an “a-ha!” moment presented itself to me. You see, I have two consumer zoom lenses:
The “a-ha!” moment goes like this: if I compare the lens opening of the two lenses at their widest, then I would get a bigger aperture opening. This can be shown by doing the math:
  • 17mm / 4 = 4.25mm
  • 70mm / 4 = 17.5mm
My heart jumped out of my chest with the realization that I, essentially, have a “faster lens” with the 70-300mm than the 17-85mm for the same f/number.

Alas, my head stepped in and calmed me down and the more rational aspect of me prevailed. So what happened? I came to the conclusion that “all f/stops of the same value are created equal - f/4 is f/4, f/5.6 is f/5.6, etc no matter what the focal length.


Refer to the diagram below. I have here a “theoretical” lens which has a maximum width of 9 units and a maximum length of 17 units, purely arbitrary numbers. Say the maximum f/stop is f/3 so this will yield an opening of 3 units when the lens is zoomed-in to 9 units, while the opening is 5 units when the lens is zoomed-in to 15 units.

What does that mean? If you look at the red arrows, which represent light beams, you can see that, whether you are at 9 units or at 15 units the light beams converge in the same manner. Simply, for the same aperture stop, the sensor is illuminated in the same way! Thus, you get the same amount of light whether the opening is 3 units or 5 units for the same f/stop.

So, for the same f/stop, the sensor is lighted in the same way whether you are at the widest focal length or at the telephoto end. The sensor is also lighted the same way when you use two lenses of different focal lengths as long as the f/stop values for the two lenses are the same.

So there really is no advantage when I use the 70mm f/4 lens (opening 17.5mm) over the 17mm f/4 (opening 4.25mm). I am actually at a disadvantageous position when I use the 70-300mm lens since I would have to have a shutter speed that should not be slower than 1/300th of a second. 

There is one advantage though: because of the bigger opening for the 70mm f/4 over the 17mm f/4, I get a much nicer bokeh -  this is great when it comes to blurring out backgrounds.

Finally, to prove the fact that you get the same illuminance for the same f/stop, I set up my camera to measure the shutter speed for a given f/stop. I used a room with a constant light source and I measured the shutter speed needed to take the picture of a white wall. I used my 17mm at f/4, measured the shutter speed, then zoomed in to 85mm at f/5.6 to also measure the required shutter speed. I switched lenses and measured the shutter speeds for 70mm f/4 and 300mm f/5.6.

The results are tabled below:

Shutter Speed Values for A 
Given Focal Length and f/Stop

f/4 f/5.6
17-85mm 18 s 14 s
70-300mm 18 s 14 s

This empirical measurement, albeit of only 4 values, prove that, for the same f/stop, no matter the focal length, the measured shutter speed will be the same. 

So, once again, the rule to be learned from this is that all f/stops of the same value are created equal!

You can find a lot of great and informative YouTube videos from AdoramaTV on this link.

Note: To read more about illuminance and f/stops, I recommend this wikipedia entry.

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