At 11:40 11/26/02, Ag Schnozz wrote:
And you thought that this was an easy answer.
So far we've got four answers:
131-134mm
135mm
141.42mm
150mm
Is SQR(100*200) actually correct? Maybe, maybe not. The SQR of
the two focal lengths does not assume a starting magnification
or angle-of-view.
My Bad on my original posting of 150mm. I therefore retract it. For
rectilinear lenses, Angle of View is directly proportional to the
arctangent of the ratio of film dimension to focal length. Now that I've
spewed the basic relationship out in text form that only a Mathematician or
Physicist can decipher, here it is in equation form using ASCII characters:
FOV = 2 * arctan( 0.5 * X / f )
FOV = Field of View
X = film dimension (can be horizontal, vertical or diagonal)
f = lens focal length
To find a focal length for a specific field of view, rearrange this
equation and the focal length for a particular film dimension and FOV becomes:
f = 0.5 * X / [2 * tan( FOV / 2)]
Thus, for field of view, approximately 135mm is half-way between 100mm and
200mm.
Now, onward to FOV and magnification. Yes, FOV and magnification
differ. Magnification is the ratio of image size to object size. It is
dependent only on focal length and object distance from the front lens
node. It is independent of film dimensions. FOV is dependent on film
dimensions and focal length. It is nearly independent of object distance
from the front lens node. However, FOV does decrease slightly as object
distance is reduced if lens focusing is achieved by moving it farther from
the film plane. It's most noticeable at macro distances with high
magnification. Why? As the lens is moved farther from the film plane, the
diameter of its image circle at the film plane increases. Not very
noticeable at non-macro magnifications (less than 1:4) as the increase is
very slight. More noticeable at macro distances (greater than 1:4) as the
increase in image circle diameter starts to become significant.
-- John
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