Pinhole Size

Why did I use a pinhole size of 0.3 mm for my pinhole camera?

One of the classical formulas to calculate the optimal diameter of the pinhole, is the one by Lord Rayleigh (this is the same Lord Rayleigh from, for example, the Rayleigh distribution, and the 1904 Nobel Prize in Physics),

d = 1.9√fλ,

where d is the diameter of the pinhole, f is the focal length and λ is the wavelength of the light. The focal length of my pinhole camera is 49 mm. For an average wavelength of light of 550 nm, this results in (all numbers converted to mm)

d = 1.9√49×0.00055 ≈ 0.31 mm.

The closest easily available size to that is, of course, 0.3 mm. So that's what I picked.

f-number

Why is the f-number of my pinhole camera f/163?

The f-number (N) is defined to be

N = f / d,

where f is the focal length and d is the aperture diameter.

The focal length of my pinhole camera is 49 mm and the aperture diameter is 0.3 mm, so in this case

N = 49 mm / 0.3 mm ≈ 163.

Aperture Difference

Why is the difference between f/163 and f/10 about 8 stops?

The relation between f-number (N) and aperture (a) is

N = √2^a.

This means that the aperture difference between f/163 and f/10 is

log_√2(163)−log_√2(10) ≈ 8.

In order to calculate this using the log button on a calculator, divide by log(√2), so

log_√2(163) = log(163) / log(√2).

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