The Cosmic Game ( PDFDrive.com )

Cosmic Game © Douglass A. White, 2012 v151207 168
Measuring the Wavelength of the Sodium D-line
In order to figure out the energy of the light and Planck's constant, the Egyptians had to
be able to measure the wavelength of the sodium "D-line" fairly accurately. (D is the
letter that modern scientists assign to the sodium spectral line.) The problem they faced
was that the visible light spectrum is all in the nanometer range. Nevertheless, the
Egyptian obsession with the accurate observation of sunlight and its various optical
phenomena made them aware of the problem of diffraction, since that had a direct
bearing on the fine measurements they had to make when using gnomon and bay tools to
determine the exact position of the sun.
They noticed that when a beam of light passed through a small slit, it caused the light to
diffract. Anyone can see diffraction easily by making a thin gap between thumb and
index finger. If you hold the two fingers fairly close to your eye and look at the blue sky
or a lit background, you will see a series of dark lines appear in the gap like a stack of
hairs. If you shine a candle light through a slit and reflect it off a CD, the disk acts as a
diffraction grating. Diffraction is caused by the interference of light waves.
Christopher Dunn has closely inspected the granite sarcophagi in the Serapeum and finds
that the Egyptians could "carve" in the hardest stone parallel walls to within extremely
fine tolerances. See Dunn's website (www.gizapower.com) with photos of him
measuring the sarcophagi and see his book, Lost Technologies of Ancient Egypt. With
such advanced machining capabilities in the cutting of extremely hard stone, for the
Egyptians to make a precise slit of submillimeter thickness, for example between two
well-polished cubit rods positioned very close together, would have been no problem.
The formula for computing the wavelength of any monochromatic light is
λ = a sin θ
Lambda (λ) is the wavelength, a is the width of the slit, and theta (θ) is the angular
position of the first minimum when a beam of sodium light encounters the slit
orthogonally and passes through with diffraction producing wave interference and a
spread.
For our example we set the slit width as .1mm (i.e., 10 -4 m).
wavelength is 589 nm for sodium light from simple trigonometry.
We know that the
(5.89e-7 m) = (.1 mm) (sin θ)
sin θ = .00588995 = 5.88995e-3
θ = .33747°
Of course, the Egyptians had to make use of their knowledge of wave behavior in water
and the science of measuring triangle relationships (trigonometry). They would make a
slit, measure the angle of the first minimum in the diffraction pattern, and then compute
the wavelength to be around 589 nanometers (588.995 and 589.5924 nm). We have
ample evidence that they were aware of the meter as a unit of measure, since it was the