#5. Focusing Distance
True or False?
Your focusing distance is approximately one-third the way between the front and back of your field of focus.
The focusing distance, in other words, is the distance to subject in focus, us.
The distance between the subject in focus, us, and the front (the near extent) of the field of focus, un, is the difference us – un. It can be compared to the depth of field to calculate how far into the field of focus does the focusing distance lie.
The depth of field is the distance between the front (the near extent) of the field of focus, un, and the back (the far extent) of the field of focus, uf. It is the difference uf – un.
Camera … un <—> us <—> uf …
The ratio of these differences, (us – un)/(uf – un), gives us the fraction of the distance through the field of focus where we find the subject in focus. This ratio can be calculated exactly from the field of focus equations that are used to calculate the depth of field.
(us – un) / (uf – un) = [(h + f) – us] / 2h = (uh – us) / 2h
This equation says that the fraction of the depth of field in front of the point of focus point is half the fraction of the hyperfocal distance behind the point of focus. The way to visualize this is to picture yourself looking at the camera from the hyperfocal distance. Picture the point of focus at a distance us from the camera along the line between you and the camera. Cut that distance in half bringing it closer to you at the hyperfocal distance. Picture the relationship of the distance to this new point compared to the distance to the camera (the hyperfocal distance). This relationship is the same as what you see when you stand at the near extent of the field of focus and compare the distance to the focusing point from where you are standing to distance across the whole of the field of focus, that is, to the depth of field.
Note well that the placement of the point of focus between the camera and the hyperfocal point determines the placement of the point of focus within the field of focus. The fraction of the depth of field in front of the point of focus varies smoothly from 1/2 when the distance to the subject is small (the point of focus is near the camera) to 0 when the distance to the subject is near the hyperfocal distance. (As the subject approaches the hyperfocal distance, the far extent of the field of focus and the distance behind the point of focus become so large that the distance in front of the point of focus becomes negligible in comparison.)
This fraction travels smoothly between 0 and 1/2 depending upon how the focusing distance compares with the hyperfocal distance. Contrary to what many photographers have been led to believe, this fraction is one-third only when us = h/3. The situation at a single point among many other points hardly makes this statement a good generalization. In fact, you are wrong almost all of the time that you use it!
Note that h = f2 / A dc = uh – f is not the true hyperfocal distance, uh, rather it is an approximation to the hyperfocal distance, uh – f ≈ uh, even though it is a rather good approximation.
The derivation and use of the Field of Focus Equations are discussed in the book Photographic Exposure Calculations and Camera Operation.
Copyright 2008 Michael G. Prais, Ph.D.
For a readable but in-depth analysis of this concept along with many other concepts associated with photographic exposure, take a look at the book Photographic Exposure Calculations and Camera Operation. This book provides insight into the equations that govern exposure, exposure meters, photosensitive arrays (both solid-state and emulsion) and the Zone System as well as concepts associated with resolution, dynamic range, and depth of field.
The book is available through Amazon.com (ISBN 978-1-4392-0641-6) where you can Search Inside!™.
Check http://michaelprais.info under Photography for the table of contents, an extensive list of the topics and subtopics covered, the preface describing the purpose of the book, and a diagram central to the concepts in the book.
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