====== Equations ======


===== Basic =====
When a lens is used to form an image of some object, the distance from the object to the lens $u$, the distance from the lens to the image (i.e. film plane) $v$, and the focal length $f$ are related by:
\[\frac {1}{f} = \frac{1}{u}+\frac{1}{v}\]
which can be rewritten as e.g.:
\[v=\frac{uf}{u-f}\]
or 
\[v=\frac{uf}{u-f}\]


Jada jada...

\[N=\frac{f}{d}\]


===== Circle of Confusion =====


==== Standard ====
^ Format    ^ CoC  ^ CoC ^
| 6 x 4.5   |      |     | 
| 6 x 7     |      |     |
| 4" x 5"   |      |     |




===== Depth of Field =====


The depth of field $d_F$ is simply the relative distance between the front and rear limits $d_f$ and $d_r$ respectively:
\[d_F = d_r -d_f\]

\[d_f = \frac{uf^2}{f^2 + c^2N(u-f)}\]
\[d_r = \frac{uf^2}{f^2 - c^2N(u-f)}\]




\[\text{DOF} \approx \frac{2u^{2}Nc}{f^{2}}\]





The depth of field, $D$, is directly related to the depth of focus, $\Delta d$, 
\[z=\frac{\Delta d}{2c}\]


fun = @(c, d) d ./ (2*c)
c_normal = 0.089
c_critical = 0.030

==== Practical use ====
A (view) camera is focused by 
  - Set focus on the most distant object in the scene for which an acceptable sharpness is still required.
       * (This object will be at... $D_{far}$
       * Jada jada...using a caliper/ruler...$d_{far}$
       * Take note on how far the lens is extended from the 
  - Set focus on the most nearby object in the scene for which an acceptable sharpness is required.
       * (This object will be at... $D_{close}$
       * Jada jada...$d_{close}$
  - Calculate, or measure, the depth of focus: \[\Delta d = d_{far} - d_{close}\]
  -