Define a plane electromagnetic wave in terms of its wavefronts and field dependence.

A vacuum plane wave has frequency \(2.40\times10^{14}\,\mathrm{Hz}\). Find its wavelength.

A wave has wavelength \(4.0\,\mathrm{cm}\) in vacuum. Find its frequency.

For a plane wave with phase \(kx-\omega t\), state the propagation direction and speed.

A wave has \(k=8.0\,\mathrm{rad\,m^{-1}}\) and \(\omega=2.4\times10^9\,\mathrm{rad\,s^{-1}}\). Decide whether its speed matches light in vacuum.

Light of vacuum wavelength \(640\,\mathrm{nm}\) enters glass with \(n=1.60\). Find its speed and wavelength in the glass.

A plane wave in a medium has \(E_0=48\,\mathrm{V\,m^{-1}}\) and \(B_0=3.0\times10^{-7}\,\mathrm{T}\). Find the wave speed and refractive index.

A wave moving in \(+z\) has \(\vec E\) along \(-x\). Determine the magnetic-field direction.

A pulse of light travels \(12.0\,\mathrm{cm}\) through a transparent block in \(0.60\,\mathrm{ns}\). Find the refractive index.

A laser goes from air into water. Its frequency is \(5.0\times10^{14}\,\mathrm{Hz}\), and water has \(n=1.33\). Find its wavelength in water and explain the invariant quantity.

Derive \(v=\omega/k\) from the condition that a fixed phase point moves with the wave.

A plane wave is written \(E_y=E_0\cos(1.2\times10^7x+3.6\times10^{15}t)\). Find its direction and speed.

A material has refractive index \(n(\lambda_0)=1.50+2.0\times10^{-4}(600\,\mathrm{nm}/\lambda_0)^2\). Which vacuum wavelength, \(400\,\mathrm{nm}\) or \(700\,\mathrm{nm}\), travels faster?

A plane-wave expression uses \(kx-\omega t\), but the stated energy flow is \(-x\). Give a model-based reason this is inconsistent for a normal plane wave.

A wave crosses from medium 1 to medium 2 with \(n_2>n_1\). Without using refraction angles, reason what happens to speed, frequency, wavelength, and wave number.

Two media have \((\epsilon_r,\mu_r)=(4,1)\) and \((1,4)\). They have the same wave speed. Do they necessarily have the same \(E/B\) ratio and impedance behavior?

A field is uniform over planes of constant \(x+y\). What is the propagation direction of the plane wave if phase increases as \(kx+ky-\omega t\)?

A light pulse travels through \(1.0\,\mathrm{m}\) of glass with \(n=1.50\), then \(1.0\,\mathrm{m}\) of water with \(n=1.33\). Find the total time and the effective average speed over \(2.0\,\mathrm{m}\).

A plane wave has electric field perpendicular to \(\hat n\), but its magnetic field has a component parallel to \(\hat n\). Use Maxwell's source-free conditions to reject or refine the model.

Prove that changing medium while keeping source frequency fixed forces a phase-matching change in wavelength at the boundary.