Is Focal Length and Field of View linear?

So the relationship between Focal Length and Field of View is not linear.

Geometrically the equation seems easy for conventional focal lengths:

α = field of view
36mm = sensor width (18 = half width)

tan( α ) = 36mm/focal lentgh and α = atan(36/fl)

(or better 2*tan(α/2) = 36mm/focal length which gives α = 2*atan(18/focal length))

But it doesn't work for UWA wider than 8mm, when the field of view is 180° or more

A great downloadable calculator:

http://toothwalker.org​/optics/vwdof.html

pwm2 wrote in post #16416859
Both a 50mm and a 100mm macro lens can capture your subject at 1:1, i.e a 5mm fly could project to 5mm on the sensor.

The difference - just as non-macro - is that the 100mm lens gives 1:1 reproduction at twice the distance from the fly. So you disturb the fly less. And - just as for normal photography - thr 100mm lens will give a narrower field of view so the background will be more magnified than when captured with the 50mm lens.

Thanks! That's what I kind of thought, but wanted to be sure.

Put this together in case anybody is interested

Units on the left are in degrees

DanAnCan wrote in post #16417198
Put this together in case anybody is interested

Units on the left are in degrees

You need to change all the "FoV" labels to "AoV" as you are dealing with degrees. Field of View is dimensional and changes for any given focal length depending on the format of the camera (size of the film frame or digital sensor).

yes I realized after posting, but you get the point...

DanAnCan wrote in post #16417227
yes I realized after posting, but you get the point...

I understand, but many newbies reading the forums may not. If you can change the graphic it would be good for those just learning.

Thanks.

For those wishing to come up with their own detailed chart for their camera, as the attached Canon Lens chart shows, the FOV angle on a lens varies depending upon sensor size. I'll leave the charting and plotting to the discretion of the reader.
http://www.usa.canon.c​om …ns_Extender_cha​rt_new.pdf