These topics are very simple conceptually, but the results can be complicated to understand intuitively.
Focal Length
"Equivalent focal length" is a very simple linear multiplier, complicated only by the different aspect ratios of different sensor formats. Modern "medium format" (Hasselblad, Fuji, some Phase one) is a 33x44mm sensor, a 4:3 aspect ratio. Compare this to 35mm "full frame" at 24x36mm with its 1.5:1 aspect ratio.
I like a 5:4 aspect ratio generally, so I crop my "full frame" to 24x30mm and my "medium format" to about 33x41.5mm when editing images. This means that an accurate focal length multiplier for equivalent focal lengths is more like
0.72x (30/41.5). If you took the same picture on each of those two cameras, from the exact same position, with equivalent lenses per this formula, you would get identically framed photographs.
(If you prefer to crop your 33x44mm images to a 1.5:1 aspect to match your "full frame" camera, then your multiplier would be 0.82x (36/44), and you'd crop your medium format shots to 29.5x44 or 1.5:1. If you don't care about aspect ratio, and just the general "feel" of the lens, then sensor diagonal is the accepted standard, so calculating 55/43 (the diagonals of the two sensors) gives you the 0.78x you mentioned. I find this a little imprecise.)
Aperture for Exposure
Aperture for exposure is simple. The f-stop of a lens is the ratio of the physical focal length to the physical size of the hole allowing light through to the sensor. So an f/2.0 lens – literally meaning focal length
(f) divided by two – has an aperture of 25mm diameter (optical designs may mean that the actual, physical aperture is different than this, but the overall design of the lens elements will create an effective aperture of exactly this size).
Aperture is the only thing that governs light passing through the sensor
(well, coatings affect it a bit, too – up to maybe 1/3 or 1/2 a stop – which is why cinematographers use transmission, or t-stops instead of f-stops, but still photographers don't worry about matching exposure between different lenses as precisely).
This means that an f/2.0 lens on
any format will require the same shutter speed and ISO for correct exposure as any other lens. The internet has invented the term, "light gathering," which is unfortunately meaningless and muddies the issue. An f/2.0 lens for a larger format, with equivalent features, will typically be larger and heavier, and depending on the flange depth of the mount, may require some tricky optical design to get good sharpness and reduce unwanted aberrations. But if the lens designers can achieve it, the illumination of a given area of the sensor of any f/2.0 lens is the same (bearing in mind that lenses for larger format sensors need to project a larger image to "cover" that larger sensor).
Aperture for depth of field
I'll preface this by saying that discussions of depth of field should really use consistent terminology. In keeping with the "depth" part of depth of field, I have always preferred "
shallower" and "
deeper" in these discussions. Not only is this the correct terminology based on two-hundred years of photography, it also accurately conveys the idea that the area of acceptable focus in front of or behind the plane of actual focus is lengthening (deepening) or shortening (getting shallower) as you "stop-down" or "open up" your aperture. And to say "more depth of field" should always mean "more" in focus; a deeper depth of field. Historically photographers cared more about depth of field as a way to ensure critical parts of the image were
in focus, as landscape photographers do today. Depth of field calculations (taking into account the size of the grain of the film, or the pixel size on the sensor as the limiting factor of how sharp any photographed element can be) allowed you to say that "from this distance to this distance everything will be rendered as sharp". Depth of field calculations didn't really have a way to quantify how "out of focus" the "not sharp" parts of the photograph would be.
(
Because of the modern tendency to equate "depth of field" with "amount of blur in the background", people have begun using "more depth of field" in a photograph to mean, "less in focus," or actually, "less depth of field". This is confusing and inaccurate.)
How aperture relates to depth of field for a given format size, focal length, and aperture is sadly, a lot more complicated. This is because it needs to account for the focus distance, which vastly affects the depth of field (the reason macro shots typically have such shallow depth of field. The equations go over my head, but smarter people than me have plugged them into online calculators, and these will help you determine the correct answers for given combinations of sensor format, focal length, and aperture.
Since when people discuss depth of field today they are as likely to mean "amount of blur behind my subject" (as do I), I find this website
http://howmuchblur.dekoning.nl to be invaluable. You can enter any combination of crop factors, focal lengths, apertures, and set subject size (from which the tool infers focus distance), and see the actual calculated size of the blur circles (
bokeh, if we must) at different distances from the subject. Because, yes, distance from the subject is another factor in how "out of focus" the background is.
This is an example of four "40mm equivalent lenses" (cropped to my preferred 4:5 aspect ratio): the Nikkor Z 40mm f/2 on a Nikon Z full-frame body; the Fujinon GF50mm f/3.5; and the new Fujinon GF55mm f/1.7, both on GFX bodies; and the Fujinon XF 27mm f/2.8 on a Fujifilm APS-C X-series body, all wide open. As you can see, the new GF55mm with its remarkable f/1.7 aperture is capable of very large blur circles, whereas the GF50mm f/3.5 cannot create blur circles even as large as the Nikkor Z 40mm f/2.
If all images were correctly exposed, and viewed at the same distance and size, they would all look identical (except for the small difference in focal length: the 55mm is a bit longer than the others relative to sensor size). The only visible differences would be the amount of subject in "acceptable" focus, and the relative size of the blur of the background.
You can actually view this graph live here and experiment with adding or changing parameters:
http://howmuchblur.dekoning.nl/#com....8-and-1.54x-27mm-f2.8-on-a-0.9m-wide-subject
BUT, you can actually kinda sum all of this up with the same multiplier as for focal length. So from the example above, the GF 50mm f/3.5 on a 33x44mm sensor can be considered a 40mm f/2.5 equivalent on "full frame" (24x30mm in my example) as 3.5 x 0.72x is 2.52. But this is only as regards depth of field, not aperture for exposure (where the 50mm stubbornly remains f/3.5).
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Part 2 follows…