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Harmonic waves 
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#1
Jul1814, 10:07 AM

P: 54

What is the difference between propagation number(K) and wave number(k) described in Optics book written by hecht
He defined K=2π/λ and k=1/λ and both of them have the same units (i.e, meter inverse) What does wave number of a Harmonic function tells about? 


#2
Jul1814, 01:54 PM

P: 789

The units look the same, but they aren't quite the same. It's a somewhat confusing notation in my opinion (especially when you use 'K' and 'k'!)
K=2π/λ is in units of radians/m and k=1/λ has units cycles/m, where "radians" and "cycles" are usually omitted. You just have to remember which kind of units you're using, so you know whether there needs to be a factor of 2π inside the sine/cosine/exponential. For example, a wave of "propagation number(K)" would be sin(Kx), while a wave with "wave number(k)" would be sin(2πkx). 


#3
Jul1814, 04:24 PM

Mentor
P: 11,787

As olivermsun noted, the units are different. ##k## is much more commonly used. ##\kappa## is mainly used by spectroscopists. I don't know if they have a practical reason for it, or if it's just a historical convention. 


#4
Jul1814, 04:45 PM

P: 789

Harmonic waves
The ##k = 2 \pi / \lambda## version is often convenient for working with waves when you also use the angular frequency ##\omega = 2 \pi / T## (where ##T## is the wave period).
That way, you can write things like ##e^{i(kx  \omega t)}## without having ##2\pi##s all over the place. 


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