Chapter 11

# To test the understanding of the lesson

## Question

A continuous laser emits in a monochromatic light beam of cross section and wavelength .

• Find the numerical values of the amplitude of the electric and magnetic fields of the Laser.

• Determine the number of photons per unit volume within the beam.

### Solution

• Power is the flux of the Poynting vector :

.

We can deduce .

The magnetic field is then given by :

• The conservation of energy gives :

Where is the Planck constant and the frequency, which is .

Finally :

## Question

Give the definition of a perfect conductor.

### Solution

The conductivity of a perfect conductor is considered infinite.

The electric and magnetic fields are zero inside a perfect conductor.

The skin thickness is assumed to be null.

## Question

Give the expression of the d'Alembert equation for a vibratory phenomenon whose wave velocity is .

### Solution

The d'Alembert's equation is, for example for the propagation of an electric field in a vacuum :

With :

## Question

• For a standing wave, defined nodes and anti-nodes.

• What is the distance between two successive anti-nodes (two nodes) ?

• What is the distance between a successive anti-node and a node ?

### Solution

• The standing wave (with ) :

The nodes are the points where the amplitude .

The anti-nodes are the points where the amplitude .

• The distance between two successive anti-nodes (two nodes) equals to , with

• The distance between a successive anti-node and a node is .

## Question

For an electromagnetic MPPW, give the relation of "structure" of the wave, that is to say the vector relationship between the vectors , and (wave vector).

### Solution

The relation of structure for a plane wave :

If the wave propagates in the direction (Oz) at the speed :

## Question

What is the speed of propagation of a MPPW in a medium of index  ?

### Solution

The velocity of the propagation of a MPPW in a medium of index is :

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