An f/2.8 lens is an f/2.8 lens. f/2.8 is a formula, referring to the focal length of the lens divided by the effective maximum aperture of the lens (usually more-or-less the diameter of the outer element on a prime lens). Thus a telephoto lens needs bigger elements than a wide angle lens for the same f/2.8 (or whatever) aperture.
I agree with you about the 24-70 2.8 on a crop sensor. You won't be able to get as shallow depth of field with a crop señor as with a ff. I think that's the point he's tying to make that you geting more like a f4 depth of field compared to a 2.8 on ff. But yes you still get the light of a 2.8 lens on a crop sensor
Depends on how you look at it. I'd argue that with the exception of the f-stop's effect on autofocus, you really don't get the light of an f/2.8 lens on a crop sensor. I mean ostensibly yes, if you have two sensors with the same pixel size and you look at a pixel-sized crop, you would see the same amount of light, but that's not the way people use cameras in practice.
People typically use cameras by framing a shot, and then viewing it at screen size or printing it at a desired print size. So the only truly interesting metric is the amount of light that makes up each square inch of output at a given size. Using that metric, because a crop sensor sees light from only about 39% of the lens, per square inch of output, a crop body gives you an image produced with only about 39% of the light that you'd get shooting the same shot with a full-frame body (ignoring any differences in light caused by moving closer to the subject, which if included, would make the crop body look even worse by comparison).
When it comes to the actual image projected on the sensor, there's no meaningful difference between using a crop body and using a teleconverter on a full-frame camera—just a little bit of IQ loss caused by the quality of the TC's glass, and maybe a tiny bit of light loss from the glass itself. And we say that using a 1.4X teleconverter makes a lens act like it is a stop slower. By that same standard, using a glorified 1.6X teleconverter (a crop body) makes a lens act like it is 1.35 stops slower. The only real exceptions to that rule are when either A. you'd be cropping the image on a full-frame to match the crop body (the reach-limited case) or B. you're talking about how the autofocus behaves. But in the more general case, you really don't get the benefits of an f/2.8 lens.
You may very well be right I don't know. I've always thought a 2.8 lens is a 2.8 lens whether it's on a ff or crop. Other than I know I'll get shallower depth of field with a ff and more depth of field with a crop at the same apertures.
It's a red herring to introduce arguments about teleconverters into this discussion. A 1.4x converter doesn't 'make a lens act as though it's a stop slower', it really is a stop slower. The 1.4x converter changes the focal length of the lens combination but it doesn't change the size of the elements so the aperture formula changes. A 50mm lens with an effective diameter of 25mm has a maximum of aperture of 50/2 or f/2. Add a 2x converter and the lens combination now has a focal length of 100mm and the same 25mm diameter gives an aperture of 100/4 or f/4. It's maths. Nothing to do with the sensor.
The central paragraph of dgatwood's post is hard to follow but the physics works like this: the aperture of a lens defines how bright the image circle on the sensor is. Whether you use most of the image circle on a full frame sensor or less of the image circle (ff lens on crop body) the brightness of the image is the same - you're just using all or part of it. There will be no impact on image quality unless the individual pixels are of different sizes - and the pixels on a ff body are usually a lot bigger than the pixels on a crop body which has both benefits and disadvantages as discussed elsewhere on this thread and others. Some people including, I think, Tony Northrup, are confusing image brightness with 'total light capture' implying that unless you can use all the light that's coming through the lens you're losing quality which is plainly not so - we don't use, nor do we want to use, the edges of the image circle because the sharpness drops off and other distortions show up more.
The topic of depth of field - shallower depth of field on a ff and deeper dof on a crop body - is another subject and an interesting one. Make an image using a ff sensor of a particular scene and observe the depth of field - how much of the scene in front of and behind the point of focus is in acceptable focus. Now crop your image in software to the equivalent size of a crop sensor (in Canon terms, that's reducing the linear dimensions by 1.6) and look at the scene that is left. The depth of field hasn't changed, of course, it's the same image - you just have less of it. Now use the same lens at the same aperture from the same taking position on a crop body and take the same picture. You will get the same image you got after cropping the ff image. And the depth of field will be the same too because you used the same lens from the same taking position. Those are the elements that affect depth of field - taking position, focus distance, focal length of the lens and lens aperture. Sensor size does not of itself affect depth of field. HOWEVER - if you switch from ff to crop and change either the focal length of the lens or the taking position so that you get the same field of view as you had for the ff image UNCROPPED then you will get more depth of field. That's not because you're using a crop sensor, it's because you're using a shorter focal length lens or you're taking the picture from further away to get the same field of view as you got with the ff sensor. Since that's how we generally use our cameras, that's how we perceive it - we get more depth of field when we use a crop camera, because we're using shorter focal length lenses to get the same pictures.
I agree that this is generally a nice explanation, particularly about light intensity. However regarding the highlighted section and on, it is wrong.
DOF relies on two factors only, physical aperture (not numerical value) and subject magnification. Aperture seems easy for most of us to understand, though we must also understand the difference between apparent physical aperture and the numerical aperture; where so many slip up is subject magnification. The print or screen size, and viewing distance, both impact DOF.
There are three situations for comparison and you have to decide which method you use because the outcome is different.
1/ Two people stand next to each other, one has a ff the other a crop camera, both have the 400 f5.6 and are shooting a nesting eagle a long way away. Both have to crop their images to get the framing they want. Obviously the ff image is cropped more but that is irrelevant, the eagle is projected on to both sensors the same size and both images are cropped to the same framing and reproduced the same size (on screen the same size) so the DOF is identical, indeed both images are identical. DOF is the same.
Same reproduction size, same physical aperture = same DOF.
2/ Both photographers decide they want to show a scene setting image and change their lenses to the widest they have, both have a 35mm f2 IS and use that to take a shot, obviously the framing is different. Both show the resulting image full screen on the same sized monitor, the crop image shows each element of the scene larger because it has less fov (framing). The DOF for the crop camera is less than the ff camera. Why is this? Because the reproduction ratio of the crop camera is higher and reproduction ratio is key to DOF. DOF is less with the crop camera.
Different reproduction size, same physical aperture = different DOF.
3/ The crop camera photographer remembers in the bottom of his bag he has an 11-22, they both stand next to each other and use the same settings, with different focal lengths to take 'the same' image. When viewed on a screen the same size the crop camera has more DOF even though it is enlarged more, why is this? Well the actual subject size on screen is the same for both images, but the aperture, although the same number, is physically smaller for the crop camera. The FF camera has a 35mm @ f10, or a 3.5mm aperture opening; the crop camera has a 35mm/1.6= 21mm @ f10, or a 2.1mm aperture opening. The smaller the apparent aperture the more dof. DOF is greater on the crop camera.
Same reproduction size, different physical aperture = different DOF.
So, as can be seen, sensor size in and of itself does not impact dof, how you choose to display that resulting capture does. You cannot disassociate end reproduction size from the dof calculation, you can make any comparison you like but you need to understand the impact of those different choices.
The DOF is not greater on crop cameras in the most common comparison because we use a shorter focal length, it is greater because we use a smaller physical aperture to achieve the same exposure settings.