#### A Brief Aside Where I Talk About Mathematics

Okay, kids, lets talk about math for a bit. Remember back in math class, when you had the cartesian coordinate system? Also known as a two lines (an X and a Y) where we could identify points that lied at some position on both lines (again, X and Y). Right? Math? Remember?

Don’t worry, I’m going somewhere with this.

Okay, cartesian coordinate system. Easy stuff. Now think back to geometry, there was another coordinate system we cared about. There was the polar coordinate system.

The polar coordinate system didn’t identify points on a plane with an X and a Y coordinate. Instead, it used an angle and a distance (from the origin). Two numbers, just as before. Placing points on a plane, just as before. They just represent different things.

An angle and a distance turned out to be very useful when doing math on and around circular things, like… well, like math people sometimes do. They also help us as a way to think about light!

We care about the distance a light is away from the subject, and we care about the angle that that light has to the subject. It’s much more useful for us to think about the light’s location in these terms than it is to think about light’s positions to the camera (“camera right”, or whatever), or in some cartesian coordinate system (Which we would do if we had to install lights into a drop ceiling grid).
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Light has a distance from the subject, and an angle to the subject. For discussion, will usually assume the subject is facing the camera.

So distance and angle. Right.

# Angle

If there is one attribute that matters the most, It’s probably the angle that light comes from. The angle of the shadows. We have high and low, front and side-lighting. We also have back-lighting, and, well, everything in between.

The combination of light from different directions adds it’s own host of complexities to the situation.

There is nothing magical about angle. No propery of placing a light that is inconcevable. One just has to learn to start paying attention to light around them, as well as working iteratively while shooting.

That said, here are some fundamental points about light angles to consider.

### Light position relative to the camera

• The closer the light is to the camera, the “smaller”, or more “flat” the lighting may appear. On-camera flashes are largely considered to be ugly, but they sure do get the job done – they don’t cast shadows on anything that’s visible in the scene. The shadows are going out at about the same angle as the perspective of the camera, so shadows don’t interfere with anything.
• Light that is perpendicular to the camera is likely to cast shadows accross the scene, and highlight the edges.
• Lighting to the side (but not all the way to the side) can highlight the depth that objects have (as opposed to “flat” on-camera lighting), as the shadows are more revealing of depth information in the objects. The further to the side a light is, the
• Most photographers put lights somewhere between on-camera and to-the-side, finding a nice balance between the subject having depth, and the subject being too “dramatically” lit. Being lit dramatically means having elements totaly bright and totally dark very near each other.
• Light going into the camera runs a lot of interesting risks, such as glare, chromatic abberation, and other technical issues that generally make images “poopy”. Light behind a subject to some degree often “wraps around” the edge, serving to separate the subject from the background visually and define the countours.

### Light position relative to the subject

• As mentioned before, light that is “on-axis” to the camera can be very flat, where one can’t easily identify depth or texture information in the subject. Even if the camera is not on-axis, depending on the texture, one can light objects to still appear flat, so long as the lighting is on-axis to the depth information of the subject. A photo of a brick building, for example, will have one wall (in shadow) appear flatter than the one with the light striking accross it, regardless the camera position.
• Light striking “accross” a surface will highlight it’s texture, as the bumps, ridges, and so on will have highlights and shadows, and the existence of these bumps are exaggerated.
• Light behind a subject may glow through translucent subjects, like paper, or make objects like hair seem to glow.
• Light behind and to-the-side has the appearance of “wrapping around” a subject, as mentioned above.

# Distance

Distance is a less intuitive beast than angle. But don’t worry, it isn’t hard.

The brightiness of a light is in a radical relationship to the distance. And, sadly, “radical relationship” is not as fun as it sounds. It involves math. Wait, wait, don’t leave! It’s easy math! Easier than that coordinate system stuff I mentioned above.

The short version is this: The closer to a light source a subject is, the brighter-er the subjet is lit.

The closer you are to a light source, the brighter it is. GOT IT. EASY.

There is another layer to this. It’s a logarithmic relationship and it works like this, for a subject and a background: If a subject is x times closer to a light source than a background, then the subject is x squared times brigher.

I’m going to diagram it with emoji.

Let’s say I have a subject (cat) 1 unit to a light source (sun), and a background (building) 1 unit from that subject, 2 units from the light source.

In this case, the building is 2 units from the light source, and the cat is 1. The cat is 2 times closer, and would be 4 times as bright as the background.

Let’s pretend, for example, that the sun is really far away. Just hypothetically speaking. Let’s say that the sun is 1000000 units from the light source, and the building is 1000001 units. 1000001/1000000 is 1.000001. So the cat is 1.000001 times closer, and 1.000002000001 times as bright. Or about 1 times as bright. Which is about the same brightness. (Not one times brighter, but the cats brightness times one. Which is ….the same as… the cat’s brightness).

In other words, if the light source is really far away, then two subjects will be lit with basically the same brightness. The closer one subject is to the light source than the other, the brigher that subject will be.

In other, other, words, the ratio of the distance to the light source is all we have to care about. We care about how much closer something is, and thus, how much (squared) brighter it is.

### In Real Life

If we have a photo with subjects at different depths (say, a group photo) and we want it to be evenly lit, then we need to back our light source up.

Let’s say we don’t want the background to be seen at all, so we can photograph our subject against solid black. We need to move our wall further away. That’s kind of hard, so instead let’s just move our light source closer to the subject. I do this all the time.

Also, light distance affects not just two different subjects, but even one subject. (Like a face! I mean a person!). A closer light source is going to have a more dramatic feel than a further one because the light is not lighting the subject evenly. The side closer to the light source wil be noticably brighter, for the highlights and the side further will be darker. It will feel like it “falls into shadow faster” although that’s not really how it works.

Lastly, the distance affects the percieved size of the light source, which matters! We’ll talk about percieved light source size next.

### Don’t Worry, We’ll come back to this.

Still confused? Relax. Coming up will be practical light setups, and exercises to practice positioning light sources.

The bigger the light, the softer it is. The smaller the light, the harder it is.

“Soft” or “Hard” light refers to the transition area between what is being lit, and what is shadow. Hard light has sharp lines for it’s shadows, like the midday sun, or a puppet show. Soft light is ‘blurry’, and transitions into shadow slower.

Soft light also brings out less texture detail, and tends to light things more evenly. It is considered great for portraiture, as it can be very flattering.

Hard light is often considered dramatic, due to it’s ability to bring out texture and detail, and cast shadows like in noir films.

### Perceived size, not just size.

You could have a light source as big as the sun, but if it’s really far away, then it’s still small to the subject, so it’s going to be a hard light source. Like… the sun. The sun is a pretty good example of this.

This is why photographers tell their accountant that they need such massive studios. It’s not just because they like high ceilings, but it’s so they can back their lights far enough away in order to get the look they want to get.

In image A, below, we are lighting the subject with a single bare flash. (and the window, technically. Ignore that, that’s just so we can see the room for context) It’s a very small light source, and would produce hard shadows. If we want to soften it up, we can put a shoot-through umbrella and fire the flash into that. The umbrella diffuses the light, and now we can see the light source in B is much larger.**

If this is too large for us, the shadows a bit too soft, what can we do? We could move it further away! Like in C. What if we want much softer light? We can move the umbrella closer, as in D, and get nice soft shadows.