Magnitude and direction of k vector

[jaus tail]

Homework Statement

A light wave of wavelength 800 nm is directed in the x-y plane at 45o. For this propagating wave, 1) what is the magnitude of the k-vector?_________rads/cm
2) what is the magnitude of the k-vector?_________rads/cm

Relevant Equations

magnitude = 2(pie)/(wavelength)

I didnt understand the question. The magnitude is 2(pie)/wavelength. I get 78500 rad/cm which is pretty wrong as guess. Where would angle come into picture?

Ref: https://www.millersville.edu/physics/experiments/062/index.php

Shouldn't direction be like i + j + k ?
So will it be like:
|k|cos30 i + |k| sin30 j + 0 k ?

 

[BvU]

I didnt understand the question.

And misread the 45 degrees ? And the fact that 1) and 2) are identical ?

I get 78500 rad/cm which is pretty wrong as guess

Says who ? I get the same. Perhaps they want to see 78540 ?

|k|cos30 i + |k| sin30 j + 0 k ?

Yes, but $\pi/4$ instead of 30.

Where would angle come into picture?

Picture has $\vec k$ pointing in $-{\pi\over 4}$ direction.

 

[jaus tail]

To be honest this is all so maths. Thanks for this. What does 78540 signify. I mean so much radians / cm.

 

[jaus tail]

Shouldn't direction be unit vector like
The vector you mentioned divided by |k|?

 

[BvU]

What does 78540 signify. I mean so much radians / cm.

I get $2\pi/$(8*10^-5 cm) = 78539.82 rad/cm

Shouldn't direction be unit vector like
The vector you mentioned divided by |k|?

If you want. One can also say that is the unit vector in that direction.

 

[jaus tail]

Thanks for the guidance.

 

[BvU]

You are welcome.