Calculating the components of an electromagnetic wave

[Luck0]

Homework Statement

An electromagnetic planewave (non-monochromatic) propagates in vacuum along the positive x axis. The electric field vector is parallel to the y axis. We know the dependence of the component E_y on the variable x at the moment t = 0:

E_y(x) = E_0\ \text{if}\ |x + a| < b
E_y(x) = 0\ \text{if}\ |x + a| > b

a/2 > b > 0

An ideal plane mirror is placed at x = 0. Find the components of the electric and magnetic field as functions of the variable at the following time instants: t_1 = a/2c,\ t_2 = a/c,\ t_3 = 2a/c.

Homework Equations

One dimensional electromagnetic planewave propagating in the positive x direction:

E = E(x - ct)
B= (1/c)E

The Attempt at a Solution

As the wave propagates in the x direction, and the electric field is in the y direction, the magnetic field only has a nonzero component in the z direction. So all I have to do is find the E_y behavior at the given times and multiply it by 1/c.

Let a = ct. Then, for any time greater than zero, the electric field is null, because a is always greater than b, and x is always positive, so |x + a| has to be greater than b. So it is a wave that exists only when t = 0 for certain values of x, and vanishes for any t > 0 or any x > b. But what is the purpose of a exercise like this if the wave does not exist at the given times?

Am I wrong? How can I use the information about the mirror?

 

[Luck0]

Anyone? I asked my professor about this question, and he said to me that |x + a| is the distance between the mirror and the wave, centered at a, and 2b is the length of the wave. But now I am even more confused.