**PINHOLE MATH**

This section is not necessary AT
ALL to do pinhole photography. It is written for people, like myself, who have
to know what is going on and why. If math bothers you, go back to the tables
and you will do fine. The **ART** is more important!

When talking about measurements for a pinhole it is easier to think in metric, as in millimeters. You already do this if you own a 35 mm camera in that your lens' focal length is sized in millimeters. A normal lens being around 50-55 mm and a telephoto being anything greater than say 100 mm A wide angle lens is from 18-35 mm and so on.

In deciding on the ideal pinhole you can go from a fixed focal length and then determine the size of the ideal pinhole or you can go from the size of the pinhole and go for the ideal focal length.

There are many factors influencing the size of the pinhole and authors will disagree as to the intensity of the effects of any particular factor. The calculations below are based in empirical observations by the author of this web site. [ie. done with actual pinholes, film and such] One factor is the color of the light. Blue light has the highest resolution and red the lowest. This affects the size of the hole. For practical purposes, we compromise on green light (560nm) to be equivalent to daylight.

Metric (mm) formula for green light
(560 nm): see **TABLE OF PINHOLE SIZE TO FOCAL LENGTH**

Focal length of lens = (size of pinhole) X (size of pinhole) X 750

if we have a pinhole of 0.4mm then

120mm = 0.4mm X 0.4mm X 750

or an ideal focal length of 120mm is found.

Constants for other types and colors of light:

Daylight (560nm) | 750 |

Blue (450nm) | 934 |

Green (550nm) | 763 |

Red (650nm) [also used for tungsten] | 647 |

Infrared (750nm) | 561 |

Now the other way round: see
**TABLE OF FOCAL LENGTH TO PINHOLE (mm)**

size of pinhole = squareroot (focal length/750)

from the previous example, we will choose a focal length of 120mm

= sqrt( 120/750)

= sqrt(0.16)

= 0.4

Just for fun let us assume you are going to use your living room for a giant pinhole and it is 15 feet from the window to the wall. How big a pinhole would we need?

25.4mm = 1 inch and 15 feet = 15 x 12 = 180 inches or 4572 mm

= squareroot(4572/750)

= 2.45 mm or about 1/10 of an inch

Remember: F# = focal length / diameter of lens opening.

This can get confusing in terms of
using a light meter, so to help out here is a normal **progression
of F numbers** past what we are used to seeing:

Since pinhole f-numbers are usually not even as in the above table, here is a formula that can help:

Bright Sunny day exposure in seconds = ((f# x f#)/ASA) x 0.0039

OR = (f#/16)^2 / ASA (gives the same answer)

If you have a hand held light meter, set it to the proper ASA and read the value at F16, then use this formula to find the exposure:

Seconds = ((f# x f#)/ASA) x (f16 exp) x 0.39 OR = (f#/16)^2 x (f16 exp)

DON'T FORGET RECIPROCITY FAILURE! -see the data sheet that came with your film

*REMEMBER each jump in F# is a halving of the amount
of light available*

*One of the neatest things about pinhole photography
is the time dilation effect.*

*Over a one-hour exposure, people and cars will disappear!*

**Why do larger formats
look sharper?**

As the size of the negative gets bigger, so does the size of the ideal pinhole for the same angle of view.

Let's calculate the total lines of resolution for each format, from 35 mm to 8x10, lines of resolution is the size of the pinhole x five for daylight. You can get a bit higher with a blue filter, but this will do for purposes of this discussion.

Format |
Focal Length |
Ideal Pinhole |
Neg Diagonal |
Lines/negative |
f-stop |

35mm |
22 |
0.171 |
43 |
1257 |
128 |

6x7 |
42 |
0.236 |
90 |
1907 |
177 |

4x5 |
74 |
0.314 |
154 |
2452 |
235 |

5x7 |
100 |
0.365 |
210 |
2877 |
273 |

8x10 |
150 |
0.447 |
308 |
3445 |
335 |

The change in negative diagonal from 35 mm to 8x10 is 7 fold, but the resolution is only 2.7 fold higher, so clearly there is a diminishing return for going to a larger size. Basically, use the largest size you are willing to carry. [and can afford the film for!] ALSO, remember the f-stop gets higher with the larger formats, so you run out of light/time at some point.

Personally, I find the 4x5 format to be near ideal. There are a large number of films available [more varied than 35 mm actually], access to roll film backs, etc. The negative is just large enough to contact print and still be visible. Enlargers are in the painful, but still possible range [8x10 enlargers are in the obscene range!]. Lastly, using a pinhole camera is already a SLOWER process, so carrying around a 4x5, though slower to use than 35, is not that much different for pinholes. [8x10 cameras need an assistant or pack animal to carry around]