Why Are F/Stop Numbers Backward?

Photographers are always going on about “What f/stop did you give it?”  This may also be expressed as: f-number,  focal ratiof-ratio, or relative aperture.  What are they talking about?

Following on from the previous post about the Color Temperature and why it seems to be a paradox.  Another bit of paradoxical photography terminology is the numbering of f/stops (Aperture).  Many beginners (and not a few professionals) have a hard time reconciling that a small f/stop actually means a wide aperture and vice versa, that the big f/stop numbers mean a smaller aperture size (hole).

All is revealed when you discover that the f/stop number is the ratio result of  focal length of lens / aperture size (Diameter).  Eg.  a 100mm focal length has it’s stop (aperture) set to a size of 20mm – that means the f/stop number is 5,  but if the aperture size was just 4mm then the f/stop number is 25!  (I used easy numbers to avoid fractions of a ratio).

Definition of Focal Ratio as a graphic
Definition of Focal Ratio as a graphic

The numbers you see/use are calculated so that a doubling or halving of light passing through the aperture (iris) occurs as you move “one full stop” in the appropriate direction.  In other words the relationship of the area of the aperture opening to allow light through is the determining factor in exposure.  So different focal lengths will need different aperture areas (sizes) to pass through the same amount of light in a given unit of time.

Standard apertures (f/Stops)
Standard apertures (f/Stops)

But this doesn’t mean that if you have set f/16 then f/8 would be twice the light amount let through.  It actually turns out that the ratio number that halves the light is 11.  Oh no!  f/8 would actually be 2 stops increase which means 4 times the light is allowed to pass.  How can this be?  Easy.  Since it is the diameter of the aperture you are using you are really making use of the area of the aperture, which historically has always been a circle but could be a square or triangle or some other shape.  If you double the diameter you have actually increased the area the aperture circle encloses by 4 times!  So what is one stop (bigger in area) than f/16, turns out that it is f/12 but for other historical reasons f/11 has been used.  The ratio numbers are a little wobbly when you do the maths but it all works out in the end.

If you have heard of a T-Stop that is an f/stop corrected for transmission loss and is typically only applicable in cinematography so that different camera lens will pass exactly the same amount of light rather than the rather loose arrangement that f/stops with still image lenses have been built with.

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Color Temperature for Light. A Paradox?

It may sound weird but “white” light is purely a construct of our vision system.  The following relates to light emitting objects, light absorbing objects work on a different principle.  We now know that there is no frequency of the electromagnetic spectrum that is the color “white”.  So how can we “see” white light (apart from after too many rums)?  After centuries of puzzling about this and numerous hypothesises that showed promise but foundered on the shoals of proof it took Sir Isaac Newton to concisely explain what was going on with the visible part of the spectrum.  He was not the first to use a prism to “split” a beam of sunlight (white) into its component frequencies but he did finally take a hypothesis and turned it into a theory where the experimental results have never been contradicted.

Prism Splitting White Light into Component Frequencies
Prism Splitting White Light into Component Frequencies

Culturally we are raised from our earliest age that hot (thermometer temperature) things are red/yellow/orange while cold has been shown to us in the hues of blue/cyan.  Backed up by the fact that various normal physical effects folor this color scheme, such as fire and ice producing these colors.  When film makers had use of color film stock they quickly discovered that the feel of a film could be perceived by the overall color given to that film and, of course, still image photographers followed suit in their images too.  And, of course, painters started making use of these color perceptions from well before the discovery of photography.  The next time you watch a movie take note of the overall color cast and how it makes you feel about the temperature of the scene.

It wasn’t for another 200 odds years after Newton that somebody took understanding of the properties of light to the next level.  Max Planck’s employer had, with the discovery of incandescent electrical lighting,  tasked him to find out what temperature to heat a light filament so that the maximum light output was partnered with a minimum of electrical energy.  After several dead ends. blind alleys and box canyons Planck hit upon the idea that unless an object’s physical temperature was at absolute zero then it was always producing some part of the electromagnetic spectrum.  It’s pretty obvious now (but not then) that the type of energy produced would change as the object’s temperature increased and eventually at some specific temperature (relative to the kind of material of the object) the energy produced would reach the visible part of the spectrum.

Planck’s next leap was to theorize what happens to a “perfect black body” object (for those that need a quick refresher on what a “black body” might look like

Electro Magnetic Spectrum with Visible frequencies highlighted
Electro Magnetic Spectrum with Visible frequencies highlighted

)  when energy was pushed into it and what energy was radiated from it.  I can only guess that he may have taken a lead from iron/steel manufacturers of the time when pyrometers had not been developed, the iron/steel makers had already twigged that the color of the melt was a very precise way of determining  when it was at the correct temperature for tapping the furnace.

But at what temperature do we start to see any “color”?  As it turns out Lord Kelvin some years prior to Planck had developed his temperature scale (using the same fifference between degrees as Celsius) to measure an object’s energy from absolutely nothing happening (Absolute zero), which in Celsius is -273°C or  −459.67°F) to some super high temperature when the material under investigation would vaporize.  Planck’s experiments showed that a dull red appeared at around 1500K and that an acceptable “white” light from an incandescent filament was around 3200K (5300.3ºF).  Now I don’t know about you but even a cool temperature such as 3200K is pretty darn hot!  And hence the apparent paradox of light temperature, the lower the K temperature the “warmer” the light produced, while the “colder” light is produced as our black body reaches temperatures in K from 5600 (9620.3ºF) and onto to 10,000K (17540ºF) on an overcast day!  And that is damn hot.  If it weren’t for the cultural norms of what is considered a hot and cold color we should be saying that a “blue” day is hot and a red day is cold, if you used Planck’s  color to temperature guide to hot and cold!

So why are we still “seeing” white light regardless of the temperature of the emitting body?  Simple, Newton was the first to show that white light is always a combination of almost equal amounts of light frequencies from the Red, Blue and Green parts of the spectrum.  Our vision system is so good at “balancing” these frequencies that even if there is a small imbalance between the frequencies we perceive it as “white”.  However, tip the scale too far in one frequency direction and you will get a color cast pervading the whole scene.  Theatre lighting designers have know this for years and apart from spot lights, stage lighting is made up of those three colors and when they want “mood” lighting it is easy to adjust the ratio of colors to achieve the desired affect on the scene you are watching.  The other alternative is to “gel” a white light with the desired color (and indeed there are color gel wheels that you can use with a white light (such as a spot light).

Kelvin Color Temps overlaid on human color perception gamut
Kelvin Color Temps overlaid on human color perception gamut

An example of where our vision system does a marvellous job of “correcting” an imbalance of frequencies is florescent lighting.  Here an examination of the output shows distinct spike in the Red, Green and Blue regions and not much in between.  Originally, the fluorescent materials pumped out more Green than the other two colors.  This doesn’t bother our vision system but it does a digital sensor and unless corrected, either automatically or manually at the time of taking the picture you will get an odd green cast to you shots.  There are other color casts from different light sources and that is why your camera’s White Balance system has so many choices.  Of course for artistic purposes you may want a cast.  The term “White Balance” is used as a historical hangover from early film makers when they would evaluate the light source and figure out, with the aid of filters, how to  “balance” the frequeicies present so that “white” light was produced  by cutting back on the offending frequency that was “out of balance” with the others.