Comment And Clarification On Apertures And Light Transmission

Moon and Cirrus Clouds in mid-afternoon. (click to enlarge)
Nikon D800E, Nikon 24-120mm f/4 lens @ 120mm; 1/200th sec. @ f/8; ISO 100

Recently I was asked to explain how apertures differ on cameras with different sized sensors.  It is pretty straightforward so here it is.  In fact, I'll cover two aspects involving apertures on different sized sensors, light transmission and depth of field.  I'll cover light transmission today and depth of field in my next post.

First, light transmission.  It is very simple; f/8 is f/8 is f/8.  No matter what sensor or film size is behind the lens, the same amount of light is getting to the sensor when set for the same aperture (of course, also with identical shutter speeds).  1/125th sec. @ f/8 with a 25mm lens on a micro 4/3 camera will be the same exposure as 1/125th sec. @ f/8 with a 300mm lens on an 8" X 10" film camera.

The lens has no idea what is behind it and the lens projects the same level of luminance on whatever is behind it, whether a wall, a piece of film or a digital sensor when set at the same aperture.  For lenses designed for small sensors that light is squeezed down (narrowly focused) by the lens to cover the very small sensor.  For large sensors or even large format film, the light is focused to project over a very large area.  But, in either case it is the same amount of light that is transmitted through a lens at the same aperture.

I better define what an aperture is to better understand why.

An aperture is the ratio of the diameter of the opening through which the light passes divided by the focal length of the lens.  That is the key fact to remember—the aperture number is a ratio. Again, the same aperture on whatever camera and lens passes the same amount of light at identical shutter speeds.

Note:  For those who are very technical in nature, I'm talking theory here and not taking into consideration light transmission loss due to number of lens elements in any particular lens, quality of optical coatings, etc., which could affect the absolute transmission of light.  That technical point is more important to video people than to still photography people.  So, please don't comment on that issue.  This is meant to be basic, instructive and theoretical in nature.

To further explain, let's take f/2.  F/2 on any lens allows the same amount of light to pass through the lens no matter what size the sensor or film—just to repeat what I said above. However, the size of the aperture opening itself will vary with the focal length of the lens.  What?  The diameter of the aperture opening has to vary with focal length of the lens as aperture designations are, again, a function of the focal length divided by the diameter of the opening.  A ratio.  

Here is an example.  Using a 50mm lens at f/2 the diameter of the the aperture opening is 25mm.  Or calculating it the other way to get what aperture number for this size opening: 50mm focal length divided by a 25mm opening = f/2.  Using a 25mm lens at f/2 the diameter of the aperture opening is 12.5mm.  That is a lot smaller opening than f/2 on a 50mm lens but the same amount of light is transmitted through that same aperture ratio due to the angle at which light is entering the lens (twice the angle of the 50mm lens) and the angle at which light leaves the rear of the lens which has to do with sensor or film size (circle of projection).

Just so happens the 50mm lens is considered the normal lens on a full frame camera and the 25mm lens is considered the normal lens on a micro 4/3 camera.  Being the same amount of light is transmitted through both lenses and both lenses have the same field of view to their respective sensors, the obvious conclusion is that the 25mm lens squeezes that same amount of light onto the smaller sensor surface to produce the same field of view.  But it is the same amount of light.

Do this if you happen to have two cameras with different sized sensors or if a friend has a camera with different sized sensor than yours.  Shoot exactly the same scene at the same ISO, shutter speed and aperture and both should look identical.  Doesn't matter which lenses you each use.

Warning:  if the exposures aren't exactly the same it is because the manufacturer is not being honest with the ISO. Take Fuji for example, as they claim their ISOs are actually about twice as fast as they really are.  In other words, ISO 200 on a Nikon (or Canon I believe) is ISO 100 on a Fuji. I've tested more than one NIkon and more than one Fuji and they all showed the same differences.  Fuji says there is more than one standard for ISOs and they use a different standard than other manufacturers.  The problem is that everyone else uses the "normal" standard.  So, again, if you are using a Fuji, your results in this little test may vary, but it is not because of the aperture.

Clear as mud?  I hope not.  Just remember f/8 is f/8 is f/8.  Doesn't matter what sensor size you are using, contrary to what some are saying.  Now go out and take some photos.

Thanks for looking. Enjoy! 

Dennis A. Mook 

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