Uniform Plane Waves Questions and Answers

Answer: C

The field extends a fraction of a wavelength into the second medium but its phase does not advance there, so no net energy crosses. Bringing a second surface within that depth lets energy tunnel across, which is the principle of the optical coupler.

Answer: D

The sum has a fixed pattern of nodes and antinodes and no net propagation, which is what a standing wave is. It is exactly what total reflection from a conductor produces, the incident and reflected waves being the two travelling components.

Answer: A

The pattern repeats every half wavelength, so nodes and antinodes alternate at quarter-wavelength intervals. Measuring the node spacing on a slotted line is the classical way of determining the wavelength and hence the frequency.

Answer: B

The standing wave ratio follows directly from the two amplitudes, and the magnitude of the reflection coefficient follows from it. The position of the first minimum relative to the boundary then gives the phase of the coefficient, completing the measurement.

Answer: C

Matching means the load impedance equals the impedance of the medium or line feeding it, so the reflection coefficient is zero. Every measurement and every power transfer arrangement aims at this condition, and a standing wave ratio of one is its signature.

Answer: D

Since the phase velocity falls by the square root of the relative permittivity and the index is the ratio of the free space velocity to it, the two are the same quantity. Glass of index 1.5 has a relative permittivity of 2.25 at optical frequencies.

Answer: A

Correct answer: the phase velocity depends on frequency

In a dispersive medium different frequency components travel at different phase velocities, so a pulse, which is a sum of many frequencies, spreads out as it propagates. That is distinct from attenuation, which reduces the amplitude without changing the shape, and it is why dispersion rather than loss sets the reach of a long optical fibre link.

Answer: B

A static magnetic field makes the medium respond differently to the two circular polarisations, so their relative phase changes and a linear polarisation rotates. It is the mechanism of the microwave isolator and a nuisance on satellite links through the ionosphere.

Answer: C

Correct answer: 41.8 degrees

\[ \theta_c = \arcsin\left(\frac{n_2}{n_1}\right) = \arcsin\left(\frac{1.0}{1.5}\right) = \arcsin(0.667) = 41.8^{\circ}. \] A critical angle exists only when the wave passes into the less dense medium, which is the case here. The 48.2 degrees offered is its complement, and this figure is the basis of total internal reflection in glass and of the light guiding in an optical fibre.

Answer: D

The two components emerge one hundred and eighty degrees apart in relative phase, which reflects the polarisation direction about the plate's axis. A quarter-wave plate, giving ninety degrees, converts linear to circular polarisation instead.