I recently explained to a friend how his 50mm lens was not actually a 50mm on his camera. And that the lens's actual focal length depends on the type of sensor size. I was surprised this was a completely alien concept to them. I know this is one of the most confusing aspects of photography.

So, what is focal length? And how can I relate it to my photos?

I always like to define the terms:

fo·cal length
NOUN
The distance between the center of a lens or curved mirror and its focus.

This is not much help, is it? Ok, let's try it again. But bear with me while I explain some technical details (nerd alert warning).

Focal length results from calculating an optical distance from the point where light rays converge ("F") to form a sharp image of an object to the digital sensor. The distance of the lens to the focal point "F" and to the subject.

In the diagram above, we can see that the focal length (f) is the distance between the lens and the focal point of the lens (F). That "i" is the distance between "F" and your camera's sensor. And finally, "o" is the distance between the lens and the object.

In other words, the focal length is related to the physical construction of the lens and the size of the camera sensor.

If you fancy some math, here is the formula to calculate the focal length of the lens:

We certainly don't need to learn the math behind it. We need to remember that we define focal length using specific distances and a 35mm sensor (or film) as a reference.

All good? Because things always get complicated…

Here is where the confusion starts. If life were easy, the description above would be perfect, and off we go. But we have invented different sensor sizes, which alter the distance "i." In doing so, it changes the result of the formula.

The diagram above shows how a smaller sensor will have to be closer to the focal point "F" to obtain a sharp image using the same lens. As a result, we will now have a different "i" distance and a different focal length.

In short, on any sensor smaller than 35mm, we will have to multiply the lens' focal length with a factor greater than 1 to obtain the 35mm equivalent focal length. The multiplying factor is provided by each camera manufacturer, and it varies between 1.5 and 1.7.

An example will be easier to understand:

A 50mm lens used on a camera with an APS-C sensor with a 1.5x multiplying factor will result in a 75mm equivalent focal length.

If we go the other way and use a medium format sensor (larger than 35mm), the conversion uses a factor lower than 1.

Focal length, angle of view and magnification

The focal length also defines the lens's angle of view and magnification. The longer the focal length, the narrower the angle of view and the higher the magnification (a telephoto lens, for example). The shorter the focal length, the wider the angle of view and the lower the magnification (a wide-angle lens, for example).

Suppose our 50mm lens gets converted to a 75mm lens by using it on a small sensor camera. In that case, it will also have a narrower angle of view and higher magnification.

As a rule of thumb, lenses used on smaller sensors will have a longer focal length than what the lens says, a narrower angle of view and higher magnification.

What about the X factor?

I wanted to also mention what some manufacturers use as measurements for their lenses. This applies to zoom lenses, usually on less expensive cameras and phones.

You have probably seen this, a camera has 10x zoom, 3x zoom, etc. We tend to identify a higher x number as a better lens that can reach out longer (telephoto). But manufacturers don't tell us that this factor, 10x, for example, refers to the lens and how it was designed. 10x refers to a lens with a factor of 10 between the shorter and the longer focal length. A zoom lens that is 10mm to 100mm will be considered a 10x zoom. And a 10mm to 40mm will be a 4x zoom. But a 25mm to 100mm will also be a 4x zoom. Do you see the problem here?

Congratulations!! You made it to the end of the article. Here's a nice picture for you :-)

From my “Robots” series. See more at www.artiscultire.ca

Five Decades Later

Focal length, or, when 50mm is 50mm?