At this point, we know what’s bigger and smaller, faster and slower. We know that f/4 is a bigger opening than f/8, and therefore lets more light in. We know that a shutter speed of 1/200 is faster than 1/100, and therefore lets less light in. We know that ISO 400 is faster than ISO 200, and therefore captures more light.
You’re with me, right? Good.
I’m about to throw a little bit of math at you, but I promise it’s only a tiny amount. No, really. All we really have to do is multiply by 2 or divide by 2. That’s easy, right? Take a deep breath. Ready? Let’s go.
How much more light does a shutter speed of 1/100 let in compared to a shutter speed of 1/200? The obvious guess is twice as much, and it’s precisely right. Any shutter speed that’s half as fast will let in twice as much light. Any shutter speed that’s twice as fast will let in half as much light. So 1/200 is half as much light as 1/100. 1/400 is half as much light as 1/200, and is therefore 1/4 as much light as 1/100. Double the bottom number means half as much light. Easy, huh?
Let’s look at ISO next. Do you think that ISO 200 is twice as much light as ISO 100? Bingo! Just like shutter speed, changing the setting by 2 means twice as much light, or half as much light. ISO 200 is half as fast as ISO 400. ISO 100 is half as fast as ISO 200, so it’s 1/4 as fast as ISO 400. Again, all you have to do is multiply or divide by 2, and you’re good.
Now aperture. Do you think f/4 is twice as fast as f/8?
Sorry, but this time it’s a tiny bit more complicated. When it comes to aperture, making the opening half as big means you’re only going to get 1/4 as much light. Making it twice as big means four times as much light. If you don’t want to know why, skip the rest of this paragraph. Our aperture is basically a circular opening. Remember back in high school, the area of a circle is pi-r-squared? Changing from f/4 to f/8 means that the radius of the opening is divided by 2. Because the area is changed by the square of the radius, the area of the opening is divided by 4. The amount of light coming in is directly related to the area of the opening, so the amount of light coming in is also divided by 4.
As it turns out, the way to cut the light in half is to change the aperture by a factor of about 1.4. In this case, f/5.6 is half as much light as f/4, and f/8 is half as much light as f/5.6.
Let me put it all into a nice tidy table, in case that’s easier to follow:
|setting||Starting setting||1/2 as much light||1/4 as much light|
Now, a tiny bit of jargon. Whenever you increase or decrease the amount of light by a factor of 2, that’s called a stop. A shutter speed of 1/400 is one stop faster than 1/200. An aperture of f/4 is one stop wider than f/5.6. ISO 100 is one stop slower than ISO 200.
In summary: for shutter speed and ISO, changing the number by a factor of 2 means twice as fast or twice as slow. For aperture, changing the number by a factor of 2 means four times as fast or four times as slow. Half as much/twice as much is really all of the math you need to know in order to be a competent photographer.
A bonus note for those of you who are vaguely mathematically inclined. Remember that I said that changing the aperture setting by a factor of 1.4 meant twice as much or half as much light? The astute reader will note that 1.4 is (approximately) the square root of 2. That’s not a coincidence.
Next lesson: How the settings play together