Focus on Focal Length and Field of View

I wanted to do a quick and dirty discussion about focal length and field of view.

There is a wonderful article here about how focal length affects portraits.

These were shot on DX (1.5 crop factor), so the fields of view would differ on FX or film, but the relative changes in field of view are what I am interested in.  These were all taken at f/5.6, although as you see the light varied quite a bit unfortunately.

16mm fisheye:


20mm


24mm


28mm


35mm


50mm


85mm


105mm


135mm


200mm


Some take-aways: there is not always a lot of difference between "adjacent" focal lengths, especially 16/20/24/28 and 85/105/135, and of course 45/50/55/60 would be almost negligible.  This is not that surprising, the ratio between the focal lengths is small.  A ratio of around 1.4 or 1.5 i.e. close to the square root of 2 seems to be a good step, because it corresponds to a crop of half the area of the original frame.  (This is the same reason why f-stops are power of the square root of 2 - you need to multiply the radius of a circle by the square root of 2 in order to double the area of the circle, and thus double the amount of light hitting the film or sensor).

Because of this, getting every single focal length is really unnecessary.  I'd suggest getting a lens set such as
20mm
28mm
50mm
85mm
135mm
200mm
300mm
Where the ratios between adjacent lenses is around 1.5.  Alternatively, you could start with
18mm
24mm
35mm
50mm
To be more efficient you could even use ratios around 2, such as
24mm
50mm
105mm
200mm

Here's a quick and dirty animation: