An electromagnetic plane wave of (angular) frequency w is traveling in the x direction through the vacuum. It is polarized in the y direction, and the amplitude of the electric field is E0.

(a) Write down the electric and magnetic fields, E(x, y, z, t) and B(x, y, z, t). [Be sure to define any auxiliary quantities you introduce, in terms of to, E0, and the constants of nature.]

(b) This same wave is observed from an inertial system S moving in the x direction with speed v relative to the original system S. Find the electric and magnetic fields in S, and express them in terms of the S coordinates: E(x, y, z, t) and B(x, y, z, t). [Again, be sure to define any auxiliary quantities you introduce.]

(c) What is the frequency & of the wave in S? Interpret this result. What is the wavelength λ of the wave in S? From w and λ, determine the speed of the waves in S. Is it what you expected?

(d) What is the ratio of the intensity in S to the intensity in S? As a youth, Einstein wondered what an electromagnetic wave would look like if you could run along beside it at the speed of light. What can you tell him about the amplitude, frequency, and intensity of the wave, as v approaches c?