I am currently studying Optics, fifth edition, by Hecht. I am presented with the plane wave in Cartesian coordinates as follows:

$$\psi(x, y, z, t) = Ae^{i[k(\alpha x + \beta y + \gamma z) \mp \omega t]}$$

I am then told that $\alpha^2 + \beta^2 + \gamma^2 = 1$. Can someone please explain why $\alpha^2 + \beta^2 + \gamma^2 = 1$?

Thank you.


1 Answer 1


Here $\alpha$, $\beta$, and $\gamma$ are the Cartesian components of the unit wavenumber vector. The wavenumber vector is $\mathbf k=(k_x,k_y,k_z)=k(\alpha,\beta,\gamma)$. The squares of the components of any unit vector sum to $1$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.