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Despite some results, this problem has not really been solved in the sense in which it was intended. The puzzlers grabbed hold of the numbers, which were really only given for illustration, and tried to derive an exact result from them. Just goes to show that science is harder than calculating, I guess. I was given this problem (without any numbers) in my diploma exam in physics - and it can be solved without any calculation, or any numerical information.
From the mathematical point of view (possibly more familiar to most Perplexus folks) the solution lies in the fact that a function with a narrow peak in the temporal domain transforms as a function which is very wide in the frequency domain (see here: http://www.med.harvard.edu/JPNM/physics/didactics/improc/intro/fourier3.html). From the physics point of view, this is the uncertainty principle: As we know that the laser pulses are extremely short, the photons' uncertainty in time must be very small, and their frequency range correspondingly wide.
Here is my original solution:
Lasers emitting ultrashort pulses in the visible range are white.
Due to the uncertainty principle, the uncertainty in energy, and hence in
frequency, is proportional to the inverse of the time uncertainty, which is of
the order of the pulse length. This gives a frequency uncertainty of
1015 Hertz, larger than the frequency range of visible light (4
1014 to 7.5 1014 Hertz).
In equations:
Δf = ΔE / h = 1 / Δt
The first equality comes from writing the energy (uncertainty) as the Plack
quantum times the frequency; the second is the uncertainty principle.
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