f/Stops & Bus Stops

Can You Tell the Difference?

Yeah, this stuff is boring...


*Introduction*
	I'll probably catch hell for this page, but to be honest, I really don't care. I can come off as somewhat arrogant at times. OK, VERY arrogant, but sometimes I just feel like smacking some sense into people. When it's one of "those" times, you'll see <THWACK>. Cool? Great. I know I feel better. *This page is really* about lighting, but we're going to touch back on some photography basics before we dig out the lights.** Inspiration for this little rant comes from a lot of sources, not the least of which are the Yahoo email discussion lists for large format, Nikon manual focus, and several about portrait photography.

*Bob's Rule #1:*
If You Don't Remember ANYTHING Else From the Math Classes You May Have Slept Though During High School , Remember the Square Root of 2
	Think I'm kidding? Take a look at the aperture scale of one of your lenses. Notice anything? Come on, sure you do... Yup, the sequence of f/stops is by a factor of the square root of 2.
	"So what?" you say... <THWACK>
	Sheesh! OK, I'll eventually give you some real life examples of how knowing about the square root of 2 will make your photographic life a lot easier. But first though, we'll cover some basics...
	The numbers on the aperture scale - the f/stops - are the ratio of the diameter of the lens opening (the iris) to the focal length of the lens. Regardless of focal length, a given f/number allows a given amount of light to pass through. Example - f/2.8 on a 300mm lens passes the same amount of light as f/2.8 on a 24mm lens, the difference is that the opening on the 300mm lens will be a LOT larger than the 24mm lens at that given f/number.
	The "modern" f/number scale sequence is: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22, 32, 45, 64, etc...
	OK, some of the numbers are rounded a bit to make it easier to read (not to mention engrave on a lens scale), but the basic relationship is a sequence by a factor of the square root of 2.
	Each number in the sequence halves the amount of light as the number before it, or doubles the amount of the light as the next higher number. Example: f/8 allows half the amount of light to pass through the lens as f/5.6, and twice as much light as f/11.
	At first glance, the concept of doubling and halving by the square root of 2 sounds stupid. Well, it does until you know about the Law of Inverse Squares. In 1766, a fellow by the name of Joseph Priestley discovered that the attraction or repulsion between two electric charges is inversely proportional to the square of the distance between them. Well, that same law applies to light, sound, or any other form of radiation. You don't have to be a rocket scientist to understand it, but I'll let the rocket scientists at NASA explain it. Click here for a great article (opens in another window). Don't worry about the part where they start to talk about how cold the Pioneer 10 Spacecraft is getting, the stuff you need to know is covered before that. Go ahead, read it, I'll wait...
	Done? Good.
	Now that we've covered f/stops, here's the obligatory bus stop:

	*See, there IS a difference!*

	So, what does this have to do with making your life easier? Well, I did promise some real world examples. Let's say you're going to take a picture of your cat (we'll call him Phred). You don't have an on-camera flash handy, but you do have a floor lamp and your camera has a built in light meter. It is a given that as soon as you have finished your set up and are ready to shoot, a cat - ANY cat - will take that as a signal to get up from his nap and leave the room. NO amount of coaxing will get him back to his former perch. Phred is no exception to this rule... Our mission - to trick Phred into thinking that were not ready to shoot when we really are. Since any self-respecting cat won't move until a nano-second before you're ready, and Phred isn't aware that we know the difference between an f/stop and a bus stop, we should be able to get off at least 1 properly exposed (and in focus) shot before he heads for the litter box and/or his food bowl. The law of inverse squares, the square root of 2, and the f/stop scale on our lens all comes into play... For arguments sake, let's assume you have a 50mm f/1.4 lens on your camera. OK, I know... NO ONE owns, much less uses, a 50mm lens anymore, but let's say that's what you've got. You also have an ISO 400 B&W film such as Tri-X, APX-400, or HP5+ loaded and ready to go.* While Phred is snoozing (and shedding) on the back of a comfy chair, we make a mental note of the approximate distance of our lamp to Phred. Looks to me to be about 6 feet. Notice how Phred's ears are starting to go back, even though his eyes are closed tight? He knows... he knows... A quick glance through the viewfinder shows a meter reading of 1/30th sec at f/2.8. That's not going to give us a lot of depth of field, we really want to stop down a bit more to f/4. We also want to keep our shutter speed right where it's at as we really don't hand hold well below 1/30th sec, regardless how well we think we do. There is no choice, either Phred or the lamp has GOT to move to get that f/4 exposure. Since we know that if we move Phred he'll be wise to our little plan, the only option left is to move the lamp. We'll have only one chance to move the lamp and get the shot before Phred escapes... The question: At what distance do we place the lamp from Phred so we can have an exposure of 1/30th sec at f/4? Hmmmmm... The lamp is 6 feet away and we read f/2.8, we want f/4.... hmmmmm....... Did you say 3 feet? If you did... <THWACK> *3 feet would have given an exposure of 1/30th sec at f/5.6 NOT f/4! Remember the link to that NASA web page which you were supposed* to read? 4.25 feet is the correct answer (6/1.414). f/4 requires twice as much light as f/2.8, NOT 4 times as much. Oops... There goes Phred, he's off to the litter box... OK, go ahead and read "Lighting 101" and you'll see why the square root of 2 is so bloody important...**
* The lens and film used in our example don't matter at all. I include it here because some people just can't comprehend a discussion about photography without meaningless details.


Lighting 101
	Lest I get anymore hate mail about my occasional sarcasm, here is an actual constructive contribution for those who are "illumination challenged". Take this for what it's worth...
	1) Watt second ratings of electronic flash units are relative. A 300 watt second unit from one manufacturer does not necessarily have the same light output as a 300 watt second unit from someone else. The 300 watt second figure is a reference to the amount of energy stored in the system and does not take into consideration flash tube efficiency and loading, the reflector, losses in cables, and a multitude of other things that effect the output level of the flash system (not to mention marketing hype).
	2) As in many things photographic, in photographic lighting, your best friend (mathematically speaking) is the square root of 2 (1.414). If you pay attention as you go along, you'll notice that many things are related to each other by a factor of that number.
	3) When establishing the lighting for a scene, strive to keep it as simple as possible. Adding lights willy-nilly will get you into trouble faster than you can imagine.
	4) There are 3 basic lighting schemes with which you must be familiar. The names are related to the positioning of the key (main) light. They are:

	a) Broad lighting - Where the key light illuminates the side of the face turned towards the camera.

	b) Short lighting - The main light illuminates the side of the face away from the camera.

	c) Butterfly lighting - The main light is placed directly in front of and above the subjects face and in line with the subjects nose. The shape of the nose shadow above the upper lip gives this lighting position it's name.
	5) For the purpose of learning the 3 basic lighting schemes, keep the fill light close to the camera on the side opposite the key light.
	6) There are a number of variations of the 3 basic lighting schemes. Don't worry about them until you have mastered the basics.
	7) Lighting ratio - Simply the ratio of the amount of light falling on the highlight side relative to the light falling on the shadow side. A 3:1 lighting ratio indicates 3 units of light on the highlight side for every 1 unit on the shadow side - it does NOT indicate a 3 f/stop difference. Knowing the "look" of 2:1, 3:1, and 5:1 ratios in the broad and short lighting schemes goes a long way in learning about lighting.
	8) When learning the 3 basic lighting schemes, use equal power settings on your main and fill lights, if they are adjustable. While you're at it, forget about umbrellas and softboxes for now, just use the basic reflectors that came standard with your lights.
	*9) Just in case you didn't* follow that earlier link to the NASA site... The law of inverse squares: I= C/D² Where C is the constant luminosity, D is the subject distance from the light source and I the intensity of light at the subject. Examples: a) Light source to subject distance of 1 foot, constant luminosity of 100, the intensity at the subject is 100.** b) Light source to subject distance of 2 feet, constant luminosity of 100, the intensity at the subject is... If you said 50, you're wrong. <THWACK> The answer is 25 (1/4). c) Light source to subject distance of 1.4 feet, constant luminosity of 100, the intensity at the subject is 50. Here is a case where our friend the square root of 2 comes into play. d) Light source to subject distance of 2.8 feet, constant luminosity of 100, the intensity at the subject is 12.5 Do you see how the square root of 2 figures into this? The relationship is just like the f/stop scale on your lens.
	10) Set your fill light first, then pose your subject. Since you know your camera position, the fill light falls into place (see 5 above). Next, set your key light. Don't worry about using background and hair lights until you know how to set the key and fill for the 3 basic schemes. The reason for setting the fill first is to help you learn the mathematical relationship of the fill and key light distances.
	11) Here is the mathematical relationship of the fill and key light at a few lighting ratios. You'll note that the actual numbers in the examples will look awfully familiar (Hint - it's that square root of 2 and f/stop scale thing again). a) 2:1 - fill illuminates shadow and highlight side with 1 unit of light, key light illuminates highlight side with 1 unit. Therefore, the highlight side is illuminated by 2 units and the shadow side by 1 unit - a 2:1 ratio. Since both units are of equal power, they must be an equal distance from the subject. b) 3:1 - fill illuminates shadow and highlight side with 1 unit of light, key light illuminates highlight side with 2 units. Therefore, the highlight side is illuminated by 3 units and the shadow side by 1 unit - a 3:1 ratio. Since both units are of equal power, the key light must be closer to the subject by a factor of the square root of 2. Example - fill light at 11 feet, the key light would be 8 feet. c) 5:1 - fill illuminates shadow and highlight side with 1 unit of light, key light illuminates highlight side with 4 units. Therefore, the highlight side is illuminated by 5 units and the shadow side by 1 unit - a 5:1 ratio. Since both units are of equal power, the key light must be half the distance from the subject as the fill. Example - fill light at 11 feet, the key light would be 5.6 feet.
	There you have it, Photo Lighting 101. Enough to ponder and play with for quite some time. Like I said, if you're learning lighting, don't bother with hair and background lights until you learn how to set the fill and key - you'll only get yourself confused. Go to a store that sells wigs and buy a cheapo styrofoam head and use it for practice. Anyone care to guess how much hate mail I get from this?


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