- #1
fluidistic
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My first question is: When a wave gets reflected over a surface, its phase gets delayed by \frac{\pi}{2} rad or \pi rad, I do not remember. How can I show this? I've access to Hecht's book on Optics but didn't find anything with the change of phase for wave's reflection. If someone could point me the exact page explaining this, I'd be glad. Any website explaining mathematically this is also welcome.
My second question is, if I send a plane wave over a perfect mirror. If the phase of the wave changes by -\pi rad after 1 reflection, the wave will cancel itself?!
I'll have the sum of \vec E (x,t)=\vec E _0 (\omega t - \vec k \vec x)+ \vec E _0 (\omega t -\vec k \vec x - \pi)=\vec E _0 [\cos (\theta )+ \cos (\theta - \pi ) ]=0. It seems obviously wrong, what do I do wrong?
My third question is, how can I show that a spherical wave became a plane wave when r \to \infty? According to http://scienceworld.wolfram.com/physics/SphericalWave.html, a spherical wave can be written under the form \frac{\psi _0}{r} \cos (\omega t -kr + \phi) while a plane wave under the form \psi _0 \cos (\omega t -\vec k \cdot \vec r + \phi). So it seems they took the limit when r \to 1?!
My second question is, if I send a plane wave over a perfect mirror. If the phase of the wave changes by -\pi rad after 1 reflection, the wave will cancel itself?!
I'll have the sum of \vec E (x,t)=\vec E _0 (\omega t - \vec k \vec x)+ \vec E _0 (\omega t -\vec k \vec x - \pi)=\vec E _0 [\cos (\theta )+ \cos (\theta - \pi ) ]=0. It seems obviously wrong, what do I do wrong?
My third question is, how can I show that a spherical wave became a plane wave when r \to \infty? According to http://scienceworld.wolfram.com/physics/SphericalWave.html, a spherical wave can be written under the form \frac{\psi _0}{r} \cos (\omega t -kr + \phi) while a plane wave under the form \psi _0 \cos (\omega t -\vec k \cdot \vec r + \phi). So it seems they took the limit when r \to 1?!