Aperture is the size of the opening within the lens thru which light can pass. It is controlled by a set of diaphragm blades which open or close as demanded. Most lenses remain wide open for metering and focus and only close down for the actual exposure. 

Aperture is often confusing because the number is "backwards". A smaller number is a larger opening which allows more light thru.


Take a look at the numbers on this 18-55mm lens (these are great little general purpose lenses for very little money). It says "1:3.5-5.6". That's the "maximum aperture" for this lens and it's "variable". It goes from a maximum of f/3.5 at 18mm to a maximum of f/5.6 at 55mm and f/3.5 is a larger aperture than f/5.6.
Note the "1" in front of the apertures. The easy way to think of it is  1/3.5 (=.29) is larger than 1/5.6 (=.18). So a larger f-stop number is a smaller aperture opening.

A smaller aperture will increase sharpness and depth of field up to a point. If the aperture is too small, generally above f/11, you start to get into diffraction limiting which can reduce image sharpness. A larger aperture reduces sharpness and depth of filed. No lens is at it's sharpest wide open. Every lens has a "best aperture". That is covered in Know your Gear.

And to really simplify things. Think of aperture like this:
A small aperture number means fewer things in focus with more light on them, and a larger number means more things in focus with less light on them. The "available light" is spread out over more things in focus. (This is not really "why" there is less light with a smaller aperture, but it is easy to remember and it *IS* how things work out in the end.)

That's really almost all you need to know.

Example of a relatively small aperture used to increase DOF.

Market St Bridge

Example of using a wider aperture to gather more light.

The stuff you really don't need to know, and might not want to:

Why do some lenses have variable apertures? If the aperture blades can open up to f/3.5 at 18mm why can't they open up that wide at 55mm? Actually they can open up the exact same size physically. The maximum physical aperture itself is not variable but the focal length is. The "1" stands for the focal length of the lens and the stated aperture is the "effective aperture" diameter. So with this lens the effective aperture varies from 18mm f/3.5mm  to 55mm f/5.6mm. This is because the focal length changes. This lens gets longer physically and "focal length" is really the distance of the objective lens to the film plane or sensor.

So how can some zoom lenses have a constant aperture?
In some constant aperture zoom lenses all of the "zooming" occurs internally. Even though the reported focal length changes the physical length of the lens does not, the actual focal length remains constant so the actual aperture remains constant. 
Did you notice the use of the phrase "effective aperture"? The effective aperture is the size of the aperture opening as it "appears" thru the objective lens. With an internal zoom lens the zoom elements between the objective lens and the aperture blades move which changes the magnification of the subject and the magnification of the aperture opening size. So you get a change in effective focal length AND a change in the effective aperture even though neither actually changed physically.

(not aperture related but relevant to the constant aperture zoom) So how can the field of view change if the actual focal length does not? Well, this is because the objective lens is not a focusing lens, it is only a "light gathering" lens. When the first focusing lens is closer to the objective lens the field of view is widest and the magnification (zoom) is the least. 
constant aperture zoom lens is expensive for a reason.

A lens with a constant focal length (prime lenses) always have a fixed maximum aperture.

If the example 18-55mm lens didn't have any change to it's effective aperture it's f-stop range would be  f/3.5 at 18mm and f/16 at 55mm.

OK, so why is f/8 the same for every focal length? If f/8 is the relationship of the effective aperture to focal length, then f/8 is a larger aperture opening for a longer focal length lens right? So why doesn't the exposure change?
This is due to the inverse square law of light intensity.  Because the light has to travel further thru a longer lens the effective aperture size must be larger. Allowing more light thru makes up for the loss of intensity caused by the increased travel distance.

The rest of the stuff you should know:

Ok, maybe you don't need to "know" it. But understanding it will help.
Every "stop" of aperture reduces the amount of light passed thru the lens by 1/2. This must be compensated for by a full "stop" of ISO (double), or a full stop of SS (half speed or twice as long), or some combination of both. Apertures start at f/1 and increase by .4x. So f/1, f/1.4, f/2, f/2.8 etc. or an even easier way to remember it is to remember 2 scales and each "doubles". The first scale starts with 1 so, 1,2,4,8,16,32. The second scale starts with 1.4 so, 1.4,2.8,5.6,11,22.

Why is this important to understand? If you remember back to the ISO lesson, ISO has to double in order to gain one stop of light, and high ISO can make an image unusable. That means an unusable ISO 3200 with a f/4 lens can be a usable ISO 1600 with a f/2.8 lens for the same scene.

This is where the fast primes shine. They are relatively "simple" and therefore cost less for a fast aperture. Plus they tend to perform very well optically and aid in getting a shallow depth of field. This is why the 35mm and 50mm primes are so often recommended.


Using Aperture Priority mode.
Take a series of pictures of the same scene while varying the aperture. Try the widest aperture, the smallest aperture, and some in the middle (around f/8). Compare the images at large resolution on your computer (50-100%) and determine at what apertures your lens works best.

Also not the differences in the Depth of Field (how much is in focus).

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