Is focal length measured relative to the sensor or the lens? [duplicate]

I'm very (very) new to photography world.. I've been trying in the past few days to explore very deeply to this world.. But the more I dived in the more confused I became.

For example most of the videos that I've seen in YouTube and a lot of articles said that the focal length is the measurement between the front lens and to the convergence point, but some said (and it sounds more sense to me) that it actually from the convergence point to the sensor, so what is the truth?

• I know the above says "angle of view", not "focal length", but they're two sides of the same coin and I think the answers there should cover exactly what you're looking for. Nov 1, 2017 at 11:26
• In the past, you could find a mark on the bottom of the camera that looks like a θ. The line is where you measure from. Short answer: the focal plane, which is where the sensor is. See petapixel.com/2012/06/01/… Nov 1, 2017 at 16:32
• @JDługosz Many if not most current cameras still have the focal plane mark. Nov 1, 2017 at 23:13
• @mattdm This question really isn't about angle of view. It's about the terminology for various points on ray diagrams, whether those ray diagrams are of collimated light form a single point source or from various points within the lens' field of view, and the difference between the usage of the same terms in optical physics versus their use in practical photography. Nov 1, 2017 at 23:49
• @MichaelClark See the original question before the edit. Nov 2, 2017 at 3:37

Focal length is the distance from the conversion point to the image plane. The image plane could be film, or a digital sensor.

For the purpose of understanding focal length, think of the lens as being a pinhole that is the focal length distance from the sensor. The further you move the pinhole away (make the focal length longer), the larger the image will be on the sensor.

However, the image also gets dimmer, since the same light that passes thru the pinhole is spread over a larger area. If you double the focal length, then objects in the image double in length and width. That means they occupy 4 times the area in the image. Because the same light is spread over 4 times the area, the result is 4 times as dim. The brightness goes inversely with the square of the focal length.

Now imagine you compensate for the dimness due to double the focal length by making the pinhole larger. (That also makes the image blurrier, but that's not the point here.) You'd have to make the pinhole area 4 times larger, which means you make it's diameter twice the size.

If you've been following all that, you can see that to get a measure of how bright the projection of a lens will be, you take the ratio of the diameter to the focal length. This is exactly what the f-stop numbers are. "f/8" literally means the diameter is the focal length divided by 8. A 50 mm and a 200 mm lens set to f/8 will both project whatever part of the scene they show at the same brightness. The 50 mm will show a wider view projected onto the same sensor. The effective opening in the 200 mm lens will be 4 times in diameter of that in the 50 mm lens.

Real lenses can still largely be thought of as pinholes for the purpose of understanding focal length and aperture. The special thing lenses with all those glass elements do is make a sharp image of the scene at a particular distance, according to how the focus adjustment is set. These lenses give you sharp focus at one distance and worse at others. Pinholes are equally sharp or unsharp over the whole distance range.

The focal length is a measurement of the power of a lens. The camera lens design is a converging lens. Its job is to project an image of the outside world onto the surface of the imaging chip (or film). This image forms in the air behind the lens. It is intercepted when it plays on the surface of objects such as film or digital sensor or a ground glass viewfinder screen. The distance, lens-to-projected image is a variable. This distance is at its shortest when the subject is at an infinite distance away. Infinity translates to “as far as the eye can see”. When the focal length of a lens is measured, the best target subject is a star. Generally this measurement is made using an instrument called an optical bench. When used, the target is an artificial star created by a light source behind a lens at the end of the optical bench.

This measurement is taken from a point called the rear nodal. This point may not be located in the middle of the lens barrel. Depending on design, the rear nodal can actually fall in the air ahead of the lens or in the air behind the lens. Or it may fall somewhere within the lens barrel. The reason for this shift in position is: a camera lens is fitted with multiple lens elements. Some have positive power (convex); some have negative power (concave). The optician’s design uses a mix of lens shapes and different densities of glass to minimizes aberrations that otherwise would degrade the image.

Now the lens has limited ability to refract (divert) the incoming light rays. These must converge to create the image. When the subject is close, the distance from lens to convergence point is elongated. This distance will be longer than the focal length, which is a measurement taken when the subject is at infinity. This elongated distance is now called the “back focus” distance.

Is focal length measured relative to the sensor or the lens?

It's measured from the lens to the point behind the lens at which collimated light striking the front of the lens converges. Hopefully this is also the distance behind the lens where the film or sensor is located. Collimated light is light from a single point source that strikes the front of the lens with parallel rays. For a point source to provide collimated light, it must be sufficiently distant from the lens to be considered at infinity.

When a lens with multiple elements is used, focal length is measured from the point a theoretical single thin lens would be located having the same refractive properties as the combined multiple elements have.

It seems you might be getting tripped up by the two different types of ray diagrams that are common. They look similar, but depict two very different things. One traces multiple rays of collimated light from a single point source at infinity. The other traces single rays striking the front of the lens from each of multiple points within the lens' field of view. In the first case, the rays converge on the sensor/film/focal plane. In the second case the rays from opposite sides of the lens cross over halfway between the lens and the sensor/film/focal plane.

...but some said (and it sounds more sense to me) that it actually from the convergence point to the sensor, so what is the truth?

Ideally, the sensor is located at the len's convergence point. That is where collimated light will be brought into focus.

Also keep in mind that the field of photography and the field of optics as a branch of physics sometimes use the same terms but give them different meanings. Calling the film/sensor plane the 'focal plane' would be incorrect in the physics lab. It is perfectly acceptable in the field of photography. That is the name that camera manufacturers have long used to reference it.

• Thank you all for your quick replies, very appreciative of that. Michael can you link a video or diagram/animation of the two things that I'm getting tripped up by? Thank you so much Nov 2, 2017 at 9:43