Lenses focal length

[Eddie Draaisma]

It's exactly the same concept and in fact the same nomenclature. Focal point = focused point = burn point, length = distance.

Thus 'focal length' == distance to burn point.

Of course.

But "Brennweite" is very easy to explain, also to kids, with only the sun ("at infinity"), a magnifying glass and some things that can burn/smoke. 

[Bjørn Rørslett]

In the "burn point", light rays are focused, thus it is the focal point of the lens. Hence we are discussing exactly the same concept, just giving its designation in another language.

No need to complicate the matter.

[Eddie Draaisma]

It is more subtle than that. You have tried to make clear already a few times on this forum that focal length is a property that has only meaning at infinity.

Sunrays from infinity => lens => burn a hole in some thing at "brennweite", it automatically, inherently "includes" infinity.

I will not complicate things over here anymore.

[Bjørn Rørslett]

No, it is the the rear conjugate distance 'v' that equals 'f' (focal length) when the front conjugate distance 'u' goes to infinity (the exact scenario you describe).

1/u+1/v=1/f (thin lens equation: internodal distance = 0)

Thus your assertion is misleading. Focal length 'f' has always "a meaning". It is a crucial component of the conjugate relationships of a lens.

[Matthew Currie]

Also the myth of increased DOF (Depth Of Field) with DF sensors: if you want to frame the same scenery with a DF sensor (compared to a FX sensor) you have to maintain a bigger distance from the subject: increased distance = increased DOF. Or the other way around: with a bigger sensor and the same focal length, you get to be closer to the subject: shorter distance = shorter DOF. QED (Quod Erat Demostrandum).

I haven't read all this thread yet, but just to address this one issue we can presume a crop is a crop is a crop.  Of course, if you take an FX picture and a DX picture with the same lens at the same distance, and crop the FX to match the DX, the two should be the same.  But if you're trying to duplicate images with the two formats without cropping, I think the DX will always have increased depth of field.

Sometimes I wonder if people are getting too tangled up in the technical details of optics and rays and theories, and forgetting that the thing we're trying to figure out is what image you'll get on the equipment you're getting it on.  Optically, the myth of increased DOF may be just that, but from the practical point of view, if you want shallower depth of field for a specific image, you'll have a harder time getting it on DX.

Since both longer focal length and shorter distance increase depth of field, and of the two, focal length has greater effect,  I can't imagine how a smaller sensor would ever result in shallower depth of field without a change in aperture.  Between an FX and DX camera, the scene will be approximately duplicated with a 50 and a 35 (and yes, I know it's only approximately).  The 50 will have shallower DOF at the same distance.  If you take a DX camera and frame a subject the same with a 35 and a 50 (disregarding, of course, the different perspective), the 50 will still have a shallower depth of field even though it is further away. 

[Bjørn Rørslett]

We are back to the crux of the matter, namely, magnification of detail. When one changes the focal length but not the position, magnification changes and with it, depth of field. If you want to compensate by moving the camera and keep the lens, you alter perspective and thereby the perceived depth of field. Either way you cannot make these matters "equivalent" when formats differ and accordingly, the entire chain of arguments is shattered. It simply is an exercise in circular reasoning.

In the old days, photographers using different formats understood these principles and selected the format suited for their task. They also, hopefully, understood the concept of empty magnification, which is in the end what constrains the image quality any system can deliver if you push it outside its limits.

[Les Olson]

"But the focal length at infinity is no more the focal length than any other.  "

Except for being the definition of focal length. Which in turn enters the definition of aperture (f-number).

. 

Yes, but that is not the point.

The lens conjugate equation gives 1/f = 1/u + 1/v, where f is focal length, u is object distance and v is image distance, measured from the principal planes.  If u is infinity, 1/f = 1/v, which is convenient, but focal length can be defined for any values of u and v.  If u is not infinity, v has to get bigger if f is to stay the same, which is what happens with a view camera.  But the equation shows also that it is possible to make u smaller without changing v by making f smaller: if f is smaller, 1/f is bigger, so 1/u +1/v is bigger, so v can stay the same although 1/u is bigger and u is smaller.   

But how can you change focal length of a lens?  Well, for any compound lens there is a simple lens of equivalent focal length.  The equivalent focal length, f, of a compound lens made up of two lenses of focal length f1, f2 is given by 1/f = 1/f1 + 1/f2 if the two lenses are in contact.  If the two lenses are separated by a distance d, 1/f = 1/f1 + 1/f2 - d/f1.f2.  If you increase the distance between the lenses the equivalent focal length falls; that is how internal focusing works. 

But the new equivalent focal length you get by changing the separation of the lenses is exactly the same "f" in the lens conjugate equation as the old equivalent focal length.  It is - key point - the infinity focal length of a different lens. 

[Bjørn Rørslett]

I feel these points can be and already are beaten to their certain death. As we don't know the internodal distances for most lenses, any equation will be just an approximation anyway. This is very evident in the near range.

I recommend looking into the finder of the camera and take the shot. It answers all questions. Also the unchanged fact that the format of the camera does not in any way alter inherent properties of the lens ,which was if one recalls, the starting point for this thread.

[Les Olson]

Since both longer focal length and shorter distance increase depth of field, and of the two, focal length has greater effect,  I can't imagine how a smaller sensor would ever result in shallower depth of field without a change in aperture.  Between an FX and DX camera, the scene will be approximately duplicated with a 50 and a 35 (and yes, I know it's only approximately).  The 50 will have shallower DOF at the same distance.  If you take a DX camera and frame a subject the same with a 35 and a 50 (disregarding, of course, the different perspective), the 50 will still have a shallower depth of field even though it is further away.

DoF is inversely proportional to the square of focal length and directly proportional to the square of distance.   The two have identical effects.  DX will always have more DoF for the same framing because of the shorter focal length. 

However, a smaller film negative has to be magnified more than a larger negative to give the same print size, so DoF is less in the print from the smaller negative.  The same is true of digital sensors, assuming - as is usually ignored - equal output resolution.  This is why the depth of field calculators use a smaller circle of confusion for DX sensors than FX. 

The upshot is that for equal framing and equal print size and output resolution you need about 1 stop wider aperture with DX to get the same DoF as with FX.  So if the DoF you want corresponds to an aperture at least one stop down from maximum, you can duplicate the FX DoF with DX (eg, 85mm on FX at f/2.8 is the same DoF as 58mm on DX at f/2).  It is only if you want a DoF that requires an aperture near maximum that you can't get the same result in DX and FX.

But the bigger you print, the smaller the DoF, so if you can't use  a bigger aperture to lower the DoF you can just print bigger (that ought to be cancelled out by people viewing larger prints from further away, which increases DoF, but in most circumstances people do not adjust their viewing distance to match print size). 

[David H. Hartman]

It's quite easy to look at a scene with the naked eye, choose the distance to set perspective, more right or left, up or down and choose a point of view. A monorail view camera is more difficult to setup than a 35mm camera and I think that's where I learned this method. I don't always do this but I do it frequently.

This crop factor thing is like trying to speak a second language while translating each word into one's native tongue. This crop factor thing should pass soon but it's currently being reinforced almost everywhere.

Dave

[Bjørn Rørslett]

"DX will always have more DoF for the same framing because of the shorter focal length.  "

Why must a photographer use a shorter lens - is it mandatory for a DX camera? Of course not. Is the assumption of "the same framing" a firm non-negotiable constraint?  Of course not, yet again.  These are not prerequisites hewn in stone and hence the assertions and any conclusions thereof are void. To wit, I could double or triple the focal length with my DX camera and step back - then I would get *less* 'DOF'. And so ad nauseam.

The circular reasoning  is riddled with unspoken assumptions and conditions that one can twist in any direction to gain support for  whatever conclusion one wants. In the longer run, this gets very boring.

[ArendV]

To me owning camera's with different sensor sizes and resolutions and different lenses - as most here on the forum I think - it is quite logical to compare them in terms of field of view, DOF, magnification and resolution for different applications like birding, macro, portraits and landscapes amongst others.

Sure every comparison has shortcomings but it helps me to pick the right camera/lens combinations for an outing. And I think the following well thought through article by dpreview at least helps in some of these considerations. http://www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care
But I am sure several of you will find significant flaws in it 

[Bjørn Rørslett]

Some stuff is better left untouched. Too many worms in it.

By all means, read and enjoy 'net discussion pro et contra at your heart's desire. As long as you get the pictures you wish, nobody should bother about your choices or the fallacious claims put forward in these debates.

[Matthew Currie]

DoF is inversely proportional to the square of focal length and directly proportional to the square of distance.   The two have identical effects.  DX will always have more DoF for the same framing because of the shorter focal length. 

However, a smaller film negative has to be magnified more than a larger negative to give the same print size, so DoF is less in the print from the smaller negative.  The same is true of digital sensors, assuming - as is usually ignored - equal output resolution.  This is why the depth of field calculators use a smaller circle of confusion for DX sensors than FX. 

The upshot is that for equal framing and equal print size and output resolution you need about 1 stop wider aperture with DX to get the same DoF as with FX.  So if the DoF you want corresponds to an aperture at least one stop down from maximum, you can duplicate the FX DoF with DX (eg, 85mm on FX at f/2.8 is the same DoF as 58mm on DX at f/2).  It is only if you want a DoF that requires an aperture near maximum that you can't get the same result in DX and FX.

But the bigger you print, the smaller the DoF, so if you can't use  a bigger aperture to lower the DoF you can just print bigger (that ought to be cancelled out by people viewing larger prints from further away, which increases DoF, but in most circumstances people do not adjust their viewing distance to match print size).

Maybe I'm getting stuck on terminology or theory or something, but if I take a DX camera, and put a 50 mm.lens on it, and take a picture of a subject, and then put a 35 mm. lens on it at the same aperture, and move the 35 mm. lens closer to the subject to duplicate the size of that subject in the given sensor size, I will get two results:  one is that of different perspective, the wider lens showing a much wider background, and the second is that the view with the wider lens will have greater depth of field. 

In other words, as far as I can see in the practical sense of what you get when you make a picture, the effects of focal length and distance do not seem to cancel out.

[Roland Vink]

It is possible to get equivalent pictures with FX and DX cameras:
- the two cameras must be shot from the same point (same perspective)
- the field of view of the lenses must be identical, for example 35mm on DX and 50mm on FX
- the entrance pupil of the two lenses must be identical, for example shoot the 35mm at f/2.8 and 50mm at f/4 (35/2.8 = 50/4 = 12.5mm)

In other words when comparing DX and FX, the DX lens must have a focal length one "stop" shorter, and the aperture must be one stop faster to compensate. This is only an approximation, one stop is sqrt(2) or about 1.4, while the difference between DX and FX is about 1.5x linear, but it's close enough for most practical purposes.

This will give two images with the same framing and same relationship between the focus plane and out of focus foreground/background (DOF, bokeh etc) This is because the two cameras are viewing the world through the same "window" - the same entrance pupil from the same position. The only difference is how the view from the window is projected onto the sensor - in one case it is projected further away over a larger area (longer focal length on bigger FX sensor), in the other case projected closer over a smaller area (shorter focal length on a DX sensor). Notice also that when the image is projected over a smaller area, the light intensity is higher, in other words the f/stop is faster.

This assumes the two lenses have similar rendering, depending on how the lens is corrected the DOF and bokeh may differ greatly even for otherwise similar focal lengths and apertures (see the thread comparing the ADS 85/1.8 with the Tamron 85/1.. This comparison also ignores differences at pixel level. If both sensors have the same pixel pitch the smaller sensor will obviously have fewer pixels, it's basically a crop of the larger sensor, which puts greater limits on how much the image can be enlarged. If both sensors have the same number of pixels, the smaller sensor obviously has smaller pixels, which means each pixel has less light-gathering capacity, may have less dynamic range etc