Focal length, explained.

When we talk about focal length in photography, what we are actually often talking about is the field of view: How much of the world in front of the camera is captured through the lens. Some people also talk about magnification, but I will not go into that here, as it relates to macro photography more than focal length.

Focal length can be described as the distance from a pinhole to the (film) plane behind it. Drawn below is a simple version of a camera, the camera obscura – or pinhole camera. When light passes through the pinhole, the image on the other side is flipped upside down and mirrored. The same happens in a camera lens and in the human eye.

perspective

The further away from the pinhole, the film plane is placed, the narrower the angle that the light travels through the hole in will be. This means that the field of view gets smaller and the image on the plane will appear more magnified. Move the plane closer to the pinhole and the angle gets wider and more of the outside world will be represented in the plane. The image below shows the angle the light travels in through the pinhole.

top

When we talk about focal length, we often talk about it in 35 mm terms. That means we are talking about the field of view, you would get on a single 35 mm film frame put in the center of the back plane of a pinhole camera.
This means that when we talk about focal length, we need to know which format the recorded image will be in, otherwise, we cannot know which field of view, we will actually get.
The image below shows a front view of an image hitting the plane of a camera obscura. The dashed boxes show three common image formats in correct aspect ratio. The 6×6 medium film format, the 35 mm film frame, and the micro 4/3 format, common in mirrorless digital cameras, such as the Olympus lineup.
The image here shows us how big a difference there actually is between the different formats and WHY we have to be aware of crop factor – the factor of which the diagonal of the format is different from that of a 35 mm frame (which is crop factor 1).
The 6×6 image has about a 1.55x longer diagonal than the one of the 35 mm frame and the diagonal of micro 4/3 is 2x shorter.
Probably the most common format today in digital SLR cameras is the APS-C format. The crop factor here is 1.5x or 1.6x smaller than 35 mm depending on the manufacturer of the sensor. I have not drawn it on the picture below, to avoid it being to clotted.

formats

Today, lenses are made specifically for all the different formats, but one thing remains the same – what the focal length written on it represents. The distance the light would have to travel in a straight line before hitting the film plane and gives the same field of view as the lens in question does on the given format.
This means that a 50 mm lens on a micro 4/3 camera gives the same image as a 100 mm on a 35 mm full frame and the same as a 155 mm on a 6×6 frame, when we talk about resulting field of view on the frame.
An example: A popular lens for the micro 4/3 format is the 12-40 mm zoom lens. This gives you a field of view corresponding to a 24-80 mm zoom lens on a full frame camera.
So, you always have to multiply or divide the focal length by the crop factor of your system, to get to a common place to talk field of view from. Multiply if your format is smaller than 35 mm and divide if it is larger.