wave vector of light is expressed as k=2pi/lambda, what does really mean? what is the need of this quantity in understanding the light, though we have E, B, Poynting vector an so on..? Would any one explain with examples. Thank you.
as we know wavelength, the length of a wave in the real space
the wave vector is the reciprocal and so is the number of waves per unit distance.
see for example Sec. 8.3 of
http://www.people.fas.harvard.edu/~djmorin/waves/electromagnetic.pdf
The wave vector gives the direction of the propagation of a light ray. As an example, if you use a laser pointer, k is parallel to the light beam. The poynting vector is parallel to k too, but it describes the energy propagation (power per square meter) or intensity, resp., whereas k gives the reciprocal wavelength (cf answer of Cornwall). E, B and k are vertical. E describes the electric field, B the magnetic induction (H-magnetic field). The poynting vector P=ExH explains that E and H are vertical to P. The wave vector is needed to describe the wave function, for instance E = Eosin(wt-kr).
k is related to the wave radian frequency omega=k*c, momentum p=h_bar*k and energy = h_bar*c*k. These physical quantities elicit all types of physical intuition: k is the rate at which waves pass a point in space (say, the observer); if you absorb the radiation (or better, reflect it for twice the effect), it transfers momentum to you just like a gas pressure.
Thank you all for clarification on my doubt. I specially thank Rüdiger Mitdank for explaining each quantity and its need clearly.
Wave vector is a vector which has specific magnitude and direction (obviously we can predict that from its name). The direction is the same as the direction of phase velocity. And its amplitude is the number of cycles per unit space.
We can think of it as period of a wave. A period is the number of cycles per unit time.In the same way in the length of lambda wavelength there exist exactly one cycle. So, In unit length there will be 1/lambda cycles. This is the magnitude of an wave vector.
Here, 2pi is a constant indicating which has not much significant. In solid state physics physicists don't use this 2pi and it doesn't matter. It's direction is also exactly same as poynting vector of an electromagnetic wave.
It also indicates the momentum of the photon or any particle in quantum mechanics. We know, P=h/lambda and h is just a constant.
So, actually wave vector plays more important role in momentum space which is inverse of our normal space (obviously, momentum space is also normal but human minds face difficulty while thinking in momentum space).
Inform me if I have mentioned any misleading information as I'm not an expert.
The wave number, k, is a measure of the spatial periodicity of a wave, i.e. the number of oscillations per length unit. It is therefore measured in m−1.
Dear Light Coherence
The wave vector---k---counts the wavenumber (number of nodes) in a particular direction.
For example for a sin(kx) is 2 nodes in a distance of 4, or 1/2 node for a unit of distance. Quora has that example with a figure, so I like it and I refer you to it!
https://www.quora.com/What-is-the-meaning-of-wave-vector-k
Nevertheless all the answers in this thread are correct!
K =2π/(wave length).
So K can be consider as phase change per unit length traverse by light( EM waves).
It is well- known that k gives direction of propagation of the wave. Another way to say is that the wave vector lives in phase space while wave length in configuration space. Both are consistent with the uncertainty principle.
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