Understanding Apertures and F-Numbers

November 30, 2015

Understanding Apertures and F-Numbers

Aperture is one of the fundamental settings when taking a picture.

The aperture size—the size of the hole in the lens—combines with the shutter speed and ISO to determine the most basic aspect of an image—it’s exposure, or how much light is involved when snapping a photo.

But the aperture setting effects an image in a way that goes beyond regulating the amount of light used to capture a scene. The aperture size also has a profound effect on the depth of field, or how much of the scene is in focus in your photo.

By controlling the aperture size, you can decide to either blur and soften the background in your photo…..

Understanding Apertures and F-Numbers

...or bring everything into sharp focus…

Understanding Apertures and F-Numbers

In other words, understanding how to work with your camera’s aperture setting is really important if you want to take control of your images.

On the surface, aperture seems to actually be a pretty easy idea to grasp: the smaller the aperture, or the hole in your lens, the more of the scene will be in focus.

And that’s kind of an intuitive idea for most people since that concept corresponds to something that we’ve probably all done at some point in our lives and that is squint our eyes to bring an object into focus.

When we squint our eyes, we are effectively reducing the size of our pupils and, basically, making the aperture of the lens in our eyes smaller. And this smaller opening helps us focus.

Squinting increases our visual focus.

The same idea holds for our camera lenses too.

But, as intuitive as this may appear, a lot of beginning photographers seem to have trouble with understanding the aperture setting. And I think that difficulty lies in the idea of f-numbers.

F-numbers, also called f-stops, are the labels that describe the size of the aperture. These f-numbers can range anywhere from f/1 to f/32 and beyond.

But the way that the f-numbers work in terms of describing the size of the lens aperture can be confusing in two ways. We’re going to look at each of these separately and see if we can find an easier way to think about these relationships.

Before we get started, I’m going to warn you upfront that we are going to be diving a bit into the nitty–gritty here. I personally like understanding the details, but if that’s not your thing, feel free to go directly to the condensed version, To put it all in a nutshell…

First, the F-Numbers and the Size of the Aperture Move in Opposite Directions

The f-numbers increase as the aperture size decreases and vise versa. So the aperture size at f/1.4 is larger than that at f/2.0 which is larger than that at f/8.0 and so on.

Understanding Apertures and F-Numbers

This relationship seems to hit people intuitively the wrong way because we are accustomed to seeing the size of an object and the number that represents that object size move in the same direction. Larger numbers correspond to larger values.

But it doesn’t work that way here. That’s because the f-numbers don’t represent the actual size of the aperture opening but are instead ratios of the focal length of the lens and the aperture diameter:

Understanding Apertures and F-Numbers

Or, to put it another way,

Understanding Apertures and F-Numbers

The idea to take away from this is that when we talk about the f-number, we’re talking about a number that’s the bottom part of the fraction that's used to determine the aperture diameter. And when you think about it that way, it makes sense that the aperture size goes down when the f-number gets bigger. Because as the bottom part of a fraction gets bigger, the value of the fraction itself gets smaller.

What’s up with the sequence of F-Numbers? They’re a bit bizarre.

The sequence of f-stop numbers can, at first glance, seem somewhat random:

Understanding Apertures and F-Numbers

But the sequence above is anything but random! In fact, this is a carefully constructed series of numbers that are designed in such a way that it makes it easy to know how a change in f-number effects the amount of light reaching your camera’s image sensor.

I know that was a long sentence! But indulge me just a little longer while I explain what I mean here.

Consider that the lens aperture is a circle and that the area of that circle determines how much light will move through our lens.

We know from geometry class, way back in the day, that the area of a circle can be determined using this equation:

Understanding Apertures and F-Numbers

where r is the radius of the circle.

Let’s say that we want to reduce this area by 50%. We want to halve the amount of light that is allowed to move through the lens and make its way to the sensor. How would we do that? What do we have to do to the radius to get that to happen?

After working through the math, I can tell you that what we have to do is divide the radius (or, equivalently, the diameter) by the square root of 2, or approximately 1.414. When you reduce the radius by dividing by the square root of 2, the area of the circle in reduced by half.

Understanding Apertures and F-Numbers

And that is exactly what is behind the sequence of f-numbers. Each of the numbers in that sequence can be found by multiplying the previous number by the square root of two, or 1.414. (By convention, the numbers are rounded to make them easier to remember.)

Understanding Apertures and F-Numbers

And since we know from above that the f-numbers are the denominators (the bottom number) of fractions, this means that each increase in f-stop has the effect of dividing the radius (or the diameter) of the aperture by the square root of two.

So what does all of this mean? It means that each successive increase in the f-number decreases the amount of light through the lens by 50%.

To put it all in a nutshell…

At the end of the day, this is what you need to know about the relationship between aperture and f-numbers:

  • The aperture size and the f-numbers go in opposite directions. The smaller the f-number, the larger the aperture size; the larger the f-number, the smaller the aperture size. If this confuses you, just remember that the f-numbers are actually the bottom number in a fraction. And, as the bottom part of a fraction gets bigger, the value of the fraction itself gets smaller.
  • Each increase in the f-number reduces the amount of light passing through the camera lens by 50%. The light that passes through at f/5.6 is 50% of what passes through at f/4 which is 50% of what passes through at f/2.8.

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