Focal length definition

There are a lot of tricks employed in modern camera lenses that cloud the simple geometry so don't even try to figure that out. For longer lenses this is done to improve image quality. For shorter lenses it is also done to allow the lens to actually work considering that most of it must be located outside of the body. Best to just think of the basic physics definition.

You could take a simple magnifying glass, hold it against a cardboard tube and hold that in front of your camera body and get an image. It wouldn't be a very good image because the magnifying glass probably isn't made very well and there would be a lot of chromatic aberration. You put multiple pieces of glass together to improve the chromatic aberration and this ends up making the lens more complex. A fixed focal length macro lens with long focal length is still a fairly simple lens. Now consider a relatively short focal length lens such as a 20mm wide angle made for a DSLR. The optical center of the lens would be right about even with the front of the body and obviously this would not be practical so the glass elements are moved much farther out from the sensor and they have to use optical tricks to make it actually work. I see this even more with modern lenses than with older designs. I used to use APS-C bodies and I still have a Sigma 10-20 zoom. 10mm focal length would put the glass inside of the DSLR body, and there are also 8-16 lenses made.

Zoom lenses, and especially lenses with image stabilization, are way more complicated. Look at the length of the latest Nikon 24-70 lens. Just looking at it you would think that it was at least 200mm focal length.

So anyway it is very hard to correlate the physical shape of the production lens with the actual focal length.

bjn70 said:

So anyway it is very hard to correlate the physical shape of the production lens with the actual focal length.

Click to expand...

Perhaps you've misunderstood the purpose of the thread, or maybe you're replying to a side issue that came up. I'm primarily interested in the definition of the focal length. It seems clear now there is a simple working definition, but the terminology in optics of the Effective Focal Length.

rybu said:

rybu said:

So anyway it is very hard to correlate the physical shape of the production lens with the actual focal length.

Click to expand...

Perhaps you've misunderstood the purpose of the thread, or maybe you're replying to a side issue that came up. I'm primarily interested in the definition of the focal length. It seems clear now there is a simple working definition, but the terminology in optics of the Effective Focal Length.

Click to expand...

+1

OP: When you posted the reply in your other post with the diagram I was thinking . . . yes . . . that's the difference. Focal Length (definition) versus Effective Focal Length. LOL.

But I'm looking at that other diagram and thinking . . . ok, how do they figure out what the Effective Focal Length is? LOL.

Ok. I'm going to go have beer now. LOL.

Take care & Happy Shooting!

rybu said:

rybu said:

So anyway it is very hard to correlate the physical shape of the production lens with the actual focal length.

Click to expand...

Perhaps you've misunderstood the purpose of the thread, or maybe you're replying to a side issue that came up. I'm primarily interested in the definition of the focal length. It seems clear now there is a simple working definition, but the terminology in optics of the Effective Focal Length.

Click to expand...

I thought you had stated the definition already- where the rays focus behind the center of the single piece of glass. If you are asking how to define focal length for a complex lens system then I did misunderstand. There may be a "center" defined by the optical formula for the glass system, I just don't know that much about it. I've read that some lens models are marked with one focal length but in reality they achieve a different focal length. Focal length and angle of view are related so maybe they have to use angle of view somehow to figure it out. I know that if you go to the eye doctor they can take the glasses that you are wearing and easily test them to determine essentially their focal length so maybe the machine does something with angles. And I suppose if you can't define the center of the optical system then you are measuring an effective focal length.

TacticDesigns said:

Tom Axford said:

For anyone interested in blurring the background, the entrance pupil also determines the maximum amount of background blur that is possible.

Click to expand...

+1

How does that work?

Click to expand...

There is a very nice way of visualising what is going on which does not require any knowledge of how the lens works. We just assume that the lens produces a good sharp image of the subject.

Consider the light rays emitted from a point in the background. The light rays are emitted in all directions from that point, but the only light rays that matter are those that enter the camera lens. Light rays that go in other directions do not enter the camera and cannot have any effect on the image obtained by the camera.



Light rays (shown in red in the diagram) travel in straight lines, so there is a cone of light rays that enter the camera. The apex of the cone is the point in the background from which the light rays are coming. The cross-section of the cone where it enters the camera is determined by the entrance pupil.

Suppose the camera is focussed on a subject plane somewhere between the camera and the background. What does it mean to say that the subject plane is 'in focus'?

The camera lens focuses light from the subject plane to form an image on the sensor within the camera. This means that light from any point in the subject plane will be focused onto the corresponding point in the image in the camera. That also means that any light ray (even if it came from some point behind the subject plane) that passes through a particular point in the subject plane will be focussed onto the corresponding point in the image.

The cone of light from the background point appears as a uniform disc of light where it crosses the subject plane. So it will appear as a similar disc in the image. The size of that disc (in the subject plane) can be worked out by simple geometry if we know the distance of the background from the entrance pupil and the distance of the background from the subject.

It is also easy to see from this visualisation that the shape of the blur will be determined by the shape of the entrance pupil.

petrochemist said:

rybu said:

A functionally useful definition that I've come across is the relationship between the field of view, sensor diameter and focal length:

FOV = 2 arctan( sensor diameter / 2 focal length )

here field of view (FOV) is the maximum angle between objects seen in the picture, as seen from wherever the camera sensor is located.

Is this effectively the definition of focal length? If so, it would seem much more reasonable for advertisers to mention the lens's field of view, rather than the focal length.

Click to expand...

That is a derived formula NOT the definition. It's also only true for rectilinear lenses there are a whole host of different formulae for the various fish-eye configurations...

My Tamron 10-20mm has a maximum diagonal angle of view of around 108° while my 10-17mm fisheye on the same camera manages a 180° diagonal angle of view. Both of these are 10mm lenses at their widest but one sees 66% more. Correlating FOV to focal length is not reliable!

Click to expand...

Which is also why FOV is not a reliable indication of light gathering ability and light intensity at the focal plane.

But some of the resident experts on this forum have the strange idea that it is...

"How much light is collected depends on the size of the aperture and the angle of view"

www.dpreview.com/forums/post/62051742

"With the same size sensor, the 35mm is collecting light from a larger field of view. Imagine the scene was just a grey card, the 35mm lens sees a larger part of the card so it would collect more light if the aperture is the same. To make sure that we don't have to redo exposure calculations according to field of view, we use relative aperture settings rather than simple aperture settings. The number we use typically on the controls (2.8, above) is the f-number"

www.dpreview.com/forums/post/62048580

"To explain this, then, yes, the effect of field of view and subject-camera distance come into play. For example, for the given aperture diameters in the OP, and assume the same exposure time and average scene luminance, then if you were to change the field of view or the subject-camera distance, the exposure would change for a given camera"

www.dpreview.com/forums/post/62048247

The dependability of f/ratio being a consistent gauge of light intensity is solely the relationship between aperture size to focal length.

rybu said:

rybu said:

So anyway it is very hard to correlate the physical shape of the production lens with the actual focal length.

Click to expand...

Perhaps you've misunderstood the purpose of the thread, or maybe you're replying to a side issue that came up. I'm primarily interested in the definition of the focal length. It seems clear now there is a simple working definition, but the terminology in optics of the Effective Focal Length.

Click to expand...

In the diagram you posted earlier the incoming light is parallel (collimated) but it needn't be. Indeed, unless the source of the light is infinitely distant it is always divergent as it reaches the lens.

The "focal length" used to specify the lens is derived from collimated light; you might also see it described as the "nominal focal length". But for most purposes the nominal focal length isn't what actually matters; it's whatever the effective focal length happens to be for the subject distance.

Note that the FOV depends on the effective focal length so, as EFL varies with subject distance there isn't actually a definite FOV associated with any lens.

Tom Axford said:

TacticDesigns said:

Tom Axford said:

For anyone interested in blurring the background, the entrance pupil also determines the maximum amount of background blur that is possible.

Click to expand...

+1

How does that work?

Click to expand...

There is a very nice way of visualising what is going on which does not require any knowledge of how the lens works. We just assume that the lens produces a good sharp image of the subject.

Consider the light rays emitted from a point in the background. The light rays are emitted in all directions from that point, but the only light rays that matter are those that enter the camera lens. Light rays that go in other directions do not enter the camera and cannot have any effect on the image obtained by the camera.



Light rays (shown in red in the diagram) travel in straight lines, so there is a cone of light rays that enter the camera. The apex of the cone is the point in the background from which the light rays are coming. The cross-section of the cone where it enters the camera is determined by the entrance pupil.

Suppose the camera is focussed on a subject plane somewhere between the camera and the background. What does it mean to say that the subject plane is 'in focus'?

The camera lens focuses light from the subject plane to form an image on the sensor within the camera. This means that light from any point in the subject plane will be focused onto the corresponding point in the image in the camera. That also means that any light ray (even if it came from some point behind the subject plane) that passes through a particular point in the subject plane will be focussed onto the corresponding point in the image.

The cone of light from the background point appears as a uniform disc of light where it crosses the subject plane. So it will appear as a similar disc in the image. The size of that disc (in the subject plane) can be worked out by simple geometry if we know the distance of the background from the entrance pupil and the distance of the background from the subject.

It is also easy to see from this visualisation that the shape of the blur will be determined by the shape of the entrance pupil.

Click to expand...

+1

This is a great explanation! Thank you for taking the time to type it out!

So . . . if I am getting this idea . . . to the camera, the out-of-focus bokeh looks like how it looks on the sensor as it would at the plane of focus, if you were able to capture an image at that plane?

The diagram is helping my visualize it!

As for the shape of the blur, that is why cutting out shapes in a piece of paper and putting it on the lens results in the bokeh taking on that shape? Basically it is becoming part of the aperture / stop?

Take care & Happy Shooting!


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TacticDesigns said:

As for the shape of the blur, that is why cutting out shapes in a piece of paper and putting it on the lens results in the bokeh taking on that shape? Basically it is becoming part of the aperture / stop?

Click to expand...

Exactly.