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Thursday, 19 August 2010 22:50

In 1678 the great Dutch physicist Christian Huygens (1629-1695) wrote a treatise called Traite de la Lumiere on the wave theory of light, and in this work he stated that the wavefront of a propagating wave of light at any instant conforms to the envelope of spherical wavelets emanating from every point on the wavefront at the prior instant (with the understanding that the wavelets have the same speed as the overall wave). An illustration of this idea, now known as Huygens' Principle, is shown below.

Probabilities and Velocities

Thursday, 19 August 2010 22:50

If two events, denoted by A and B, are mutually exclusive and have the individual probabilities P(A) and P(B), then the probability of "A or B" is just the sum of the individual probabilities, i.e.,

The Hydrogen Atom

Thursday, 19 August 2010 22:48

In 1885 a Swiss secondary school teacher named Johann Jacob Balmer published a short note (entitled “Note on the Spectral Lines of Hydrogen”, Annalen der Physik und Chemie 25, 80-5) in which he described an empirical formula for the four most prominent wavelengths of light emitted by hydrogen gas. These wavelengths had been measured with great precision by Vogel and Huggins, giving the four values 6562.10, 4860.74, 4340.10, and 4101.20 Angstroms (10^-¹⁰ m). Balmer's note does not make clear whether he was also aware of the measured series limit, l_¥ = 3645.6 A, or whether he deduced this himself. In any case, one can find by numerical experimentation that the four characteristic wavelengths are closely proportional to the following products of small primes

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