# Harmonic waves

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?

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olivermsun
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).

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jtbell
Mentor
[Hecht] defined [propagation number] K=2π/λ and [wave number] k=1/λ
You have it backwards. He defines the propagation number as ##k = 2 \pi / \lambda## (lower-case Latin letter "k") and the wave number as ##\kappa = 1 / \lambda## (lower-case Greek letter "kappa", not upper-case Latin letter "K"). Those different symbols (##k##, ##\kappa##, and ##K## in LaTeX; or k, κ, and K in PF's default font) tend to confuse people. Look carefully!

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.

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olivermsun