This document is also available in a "table" (Netscape) version.

Written by Bruce Barrett (I can be reached at )

    Format
   (inches)   Format (mm)   Focal    Circle of          Hyperfocal
 Vert. Horiz. Vert.Horiz.  length &  Confusion   f-stop  distance   Equiv.
                           Diagonal   at film    number             f-stop
                            (mm)     plane (mm)          (meters)
 ---- ------  ----- ----   ---------  ---------  ------  ---------- -------
               24    36        43.27   0.024724    8          9.46       8
               60    70        92.20   0.052683    8         20.17      17
   4     5     102  127       162.64   0.092937    8         35.58      30
   5     7     127  177.8     218.50   0.124857    8         47.80    40.5
   8    10     203  254       325.28   0.185874    8         71.15      60
 ---- ------  ----- ----   ---------  ---------  ------  ---------- -------
  Calculations numbered:      1          2         3         4         5

Circles per diagonal: 1750

1. A "normal" lens has a length equal to the diagonal of the film format.
2. As long as the circle of confusion on a print is the same, the depth of focus is the same.
3. To get the same size circle of confusion on a print you need only make sure the same number of circles of confusion occupy the diagonal on the negative.
4. These calculations manage to "ignore" the negative to print magnification issue because, as long as the same number of circles of confusion can be placed "shoulder to shoulder" across the diagonal of the negative the prints will look the same (in terms of depth of focus.)
5. When focused at the hyperfocal distance everything from infinity to 1/2 the hyperfocal distance is in focus.

These are the calculations used in the table:

1. Focal length and negative diagonal = sqrt(Horiz.^2 + Vert.^2)
2. Circle of confusion (COC) = diagonal / constant (1750 in these calculations) Changing the COC number does change the hyperfocal distance but does not effect the relative f-numbers needed to achieve the same DOF, for a given film size.
3. f-stop number (constant, but in the spread sheet you can adjust it until the hyperfocal distances match)
4. Hyperfocal distance = (focal length / (f-number * circle of confusion at film plane) )/1000 All units in mm, except Hyperfocal distance which is converted to meters by the "/1000")
5. The Equivalent f-stop was determined by adjusting the f-stop number in the spread sheet until the hyperfocal distance matched 35mm, f-8 (9.46m)

Notes:

• The circle of confusion gets larger as the format gets larger.
• This reflects the fact that larger formats do not need to be enlarged as much in the final print.

Results:
When focused at the Hyperfocal distance...

• Going from 35mm to 6x7 changes the hyperfocal distance (at f-8) from 9.5m to 20.2 meters.
• Going from 35mm to 4x5" changes the hyperfocal distance (at f-8) from 9.5m to 35.6 meters.
• To get the same DOF on a 6x7cm negative as a 35mm negative you need to stop down about 2 stops (f8 to f17, yes 17, close to 16)
• To get the same DOF on a 4x5" negative as a 35mm negative you need to stop down about 4 stops (f8 to f30, yes 30, close to 32.)
• To get the same DOF on a 8x10" negative as a 35mm negative you need to stop down about 8 stops (f8 to f60, yes 60, close to 64.)

Conclusion:

• As negative size increases the COC can increase - linearly.
• As the negative size increases the lens length needs to increase linearly.
• As the lens length increases the DOF is reduced by the square of the change.
• Therefore DOF is reduced faster than the smaller enlargement advantage can compensate for and DOF is less in larger format photography.
  

I've been over this quite a few times - I think I've got it right, but if you disagree I'd love to here from you. I can be reached at I can be reached at
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