If, instead of field of view, you want the hyperfocal distance halfway
between that for 100mm and 200mm focal lengths, then the answer is 141mm
(square root of two times 100mm).
Hyperfocal distance is directly proportional to the square of the focal
length. This presumes you are not changing the camera->subject distance,
the lens aperture f-number, size of film, or maximum allowable circle of
confusion diameter.
I mention this so you will understand why I asked about what aspect of the
optics you want to know is effectively half-way between the two. The
relationships among some aspects of them are linear, but some are
non-linear as with hyperfocal distance.
-- John
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