Course content

Indicate which statements are true:

Question

The longer the lifespan of a wave front, the more monochromatic the light.

Solution

True.

Question

The longer the lifespan of a wave front, the weaker the frequency.

Solution

False, they are not related. However, the longer the lifespan of the wave train, the more the source is monochromatic and the narrower the spectrum.

Question

The longer the lifespan of a wave front, the larger the coherence length.

Solution

True, \(l_c = c\tau_c\)

Question

In emptiness, the triad \((\overrightarrow{k}, \overrightarrow{E}, \overrightarrow{B})\) is orthogonal for an electromagnetic wave.

Solution

In vacuum \((\overrightarrow{E}, \overrightarrow{B}, \overrightarrow{K})\), form an orthogonal triad; the statement, therefore, is true for \((\overrightarrow{k}, \overrightarrow{E}, \overrightarrow{B})\) and \((\overrightarrow{B}, \overrightarrow{k}, \overrightarrow{E})\).

Question

A parallel beam of light represents a plane wave.

Solution

True, according to Malus's theorem, the rays that form the energy trajectory are perpendicular to the wave surfaces.

Question

Wave surfaces contain light rays.

Solution

False , the waves are perpendicular to the wave surfaces.

Question

Quasi monochromatic light has a large spectrum.

Solution

False, it is a narrow spectral line.

Question

The coherence length of a quasi monochromatic laser (gas) source \(\Delta \lambda \simeq 10^{-6} ~\mbox{nm}\) is large, up to several meters.

Solution

True, in this case if we take \(\lambda_0 = 633~nm\) (\(HeNe\) laser) and a lorentzian spectrum, the order of width is: \(l_c = 0.318 \lambda^2 / \Delta \lambda = 0.318 \times 633^2 / 10^{-6} \simeq 127~\mbox{m}\)

Question

A wave surface is the site of all points where the electrical field vectors oscillate at the same phase (modulo \(2\pi\) )

Solution

False, a wave surface is the locus of points where the electrical field vectors oscillate strictly in phase. Vectors with a phase differing by \(2\pi\) belong to 2 different wave surfaces distant from \(\lambda\).

Question

Two wave surfaces at a distance of \(2 \lambda\) oscillates at the same phase (modulo \(4 \pi\) )

Solution

True for the same reason as in the previous question.

Question

Two polarized rectilinear waves whose polarization directions intersect at an angle of \(90˚\) can interfere.

Solution

No because two perpendicularly polarized waves do not interfere.

Question

Two polarized rectilinear wave whose polarization directions intersect at an angle of \(45˚\) can interfere.

Solution

Yes, but the average intensity of the interference figure is weaker than if the polarizations were parallel.

Question

The fringe contrast of interferences is the greatest when the two sources have the same intensity.

Solution

True, in order for the contrast to be the greatest, the complex amplitudes associated to each source must be equal.