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The Mathematical Secret Behind Your Camera’s Aperture

by Mike Perlman | December 7, 2011December 7, 2011 6:00 pm PDT

The aperture is one of the primary sources of consternation for most photographers. It’s bad enough that we have to compute shutter speed/aperture ratios, but understanding the mathematical principals behind an aperture and how it works is like decoding hieroglyphics to any beginner. I’m here to break it down for you, to the best of my ability. However, I’m not much of a math wizard, so I called upon seasoned photographer Matt Cole, who published a webpage about apertures back in 2002 called “A Tedious Explanation of the F/Stop.” To this day, Matt’s page is the most helpful reference I could find regarding aperture and other photographic skills. He was even kind enough to impart some of his genius to me over the phone. Be sure to check it out for a more in-depth look.

The aperture is made up of a set of expandable and contractable metal blades in the camera’s lens that form a hole. This hole is responsible for letting light onto the camera’s sensor. Opening that hole up wide lets the most amount of light onto the sensor while closing the hole down lets the least amount of light onto the sensor.

Aperture-Diagram

Diagram of an 8-Bladed Aperture

The opening of the aperture’s hole is measured by F/Stops. As shown above, F/Stops are usually displayed on a camera’s lens and increase in value. According to this particular lens, at F/3.5, the aperture is opened up to its widest hole while at F/32, the aperture will be closed down to the smallest possible hole. Why is it that the larger the number, the smaller the hole?

It’s because F/Stops are a ratio of two things: the diameter of the aperture in the lens and the focal length of the lens. For instance, if we had a lens at a 135mm focal length, adjusting the aperture to F/3.5 would mean the aperture (hole) is open 38.6mm (135/3.5 = 38.6). A 135mm lens at F/22 would mean that the aperture is open 6.1mm (135/22 = 6.1). Therefore, the higher the F/Stop (aperture value) the smaller the hole, while the lower the F/Stop the wider the hole.

Traditional apertures double or halve the light. As an example, F/2.0 is twice as bright as F/2.8. F/11 is twice as bright as F/16. The following sequence is the standard for aperture values:

F/1.4   F/ 2.0   F/ 2.8   F/ 4   F/ 5.6   F/ 8  F/ 11   F/ 16   F/ 22

As you look at the above F/Stop sequence, think wide –> narrow. An F/1.4 lens is regarded as a very bright or fast lens while an F/22 lens is regarded as a slow lens. The aperture ratio sequence is the same as the shutter speed sequence. Shutter speeds double and halve in stops, allowing twice the amount of light in or cutting twice the amount of light in half.

The aperture is the size of the hole that light passes through to hit the sensor. The shutter speed is the amount of time the aperture stays open. 

Here’s a standard shutter speed sequence:

8 seconds   4 seconds    2 seconds    1 second    1/2 second    

1/4    1/8    1/15    1/30    1/60    1/125    1/250    1/500    1/1000

There’s a caveat here. Fast (bright) lenses let lots of light into the shot and let us shoot at faster shutter speeds to minimize blur. For instance, on my Canon PowerShot S100, I can set the aperture to F/2.0 and the shutter speed to 1/100 in a typical shooting environment. If I then set the aperture to F/8.0, I’d have to adjust the shutter speed to 1/8 to compensate for the aperture’s smaller hole, which is letting less light in. This basically means that the shutter is open longer to let more light in rather than the aperture being opened wider to let more light in. The shutter speed/aperture team is a ratio.

And now for the caveat: Depth of Field. It’s great that an F/2.0 lens will let the light come pouring in and allow you to shoot at faster shutter speeds to avoid image blur. But that comes at a price. Traditionally, the F/2.0 lens has a shallow depth of field, meaning the lens will only be able to focus on objects in the foreground or background, but not everything at once. Many portrait shots are captured with bright lenses because the background does not have to be in focus, and the blurred background even adds an artistic effect to the image.

Here’s an image I took at F/3.5 with the Pentax K-7, focusing in the middle of the flower while the pedals of the flower in the foreground and bee in the background are out of focus:

pentax_k-7_s03

As you can see, only the center of the flower is focused. Here’s a shot taken with the Pentax K-2000 at a much more narrow aperture, somewhere in the F/22 range:

pentax_k2000_s010

In the second shot, everything is in focus, from the rocks on the shore to the farthest building behind the Brooklyn Bridge. Although it helped that I was farther away from my subject, the F/22 aperture ensured me that everything would be in focus. If I had used a much narrower aperture, say around F/22 with the picture of the flower, everything would be in focus, from the pedals to the bee.

But there’s another caveat here as well. Depth of field all depends on the size of the camera’s sensor and your distance from the subject, in addition to the camera’s aperture. One thing you’ll notice on a typical point-and-shoot is that it has a small aperture range. Most only go up to F/8. This is because the aperture in a point-and-shoot camera is tiny compared to that of a DSLR lens, and it would be too difficult for manufacturers to achieve such a small hole with such a small aperture configuration. However, most point-and-shoots have a fantastic depth-of-field because of the smaller camera sensors and shorter lenses. As a general rule, shorter focal lengths have greater depths of field.

We’ll get into depth-of-field and focusing in another edition at a later date, but be sure to leave any questions, comments or concerns in the comment section. For more in-depth explanations, be sure to visit Matt’s page at http://www.uscoles.com.

 


Mike Perlman

Mike Perlman grew up in Nintendo Land and developed a relationship with all things electronic and nerdy early on in his childhood career. Today,...

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