- #1
wtronic
- 10
- 0
well, i have been going over this problem for about 4 hours and everytime i get closer and closer to some answer but I am never convinced i am right.
THE PROBLEM:
let lambda be the wavelength of light propagating in the x-y plane at an angle theta with respect to the x-axis in the (x,y,z,t) frame. What is its wavelength and direction of propagation in the (x',y',z',t') frame.
I know the wave equation for a wave is
[tex]\Phi[/tex]cosK[x + ct]
but since traveling at an angle, theta should I put?
[tex]\Phi[/tex]cosk[xcos[tex]\theta[/tex] +ct]
+
[tex]\Phi[/tex]cosk[ycos[tex]\theta[/tex] +ct]
and using Lorentz's tranformation
x' = [tex]\gamma[/tex](x - vt)
t' = [tex]\gamma[/tex](t - ux/c^2)
I would appreciate any help, thanks
THE PROBLEM:
let lambda be the wavelength of light propagating in the x-y plane at an angle theta with respect to the x-axis in the (x,y,z,t) frame. What is its wavelength and direction of propagation in the (x',y',z',t') frame.
I know the wave equation for a wave is
[tex]\Phi[/tex]cosK[x + ct]
but since traveling at an angle, theta should I put?
[tex]\Phi[/tex]cosk[xcos[tex]\theta[/tex] +ct]
+
[tex]\Phi[/tex]cosk[ycos[tex]\theta[/tex] +ct]
and using Lorentz's tranformation
x' = [tex]\gamma[/tex](x - vt)
t' = [tex]\gamma[/tex](t - ux/c^2)
I would appreciate any help, thanks