# Electromagnetic waves

# Radiation pressure (corpuscular calculation)

Take 20 minutes to prepare this exercise.

Then, if you lack ideas to begin, look at the given clue and start searching for the solution.

A detailed solution is then proposed to you.

If you have more questions, feel free to ask them on the forum.

The energy and the momentum of a photon are given respectively by :

and

Where is a unit vector directed in the direction of propagation, Planck's constant and the speed of light in vacuum.

Assume the isotropic and monochromatic solar radiation, average wavelength .

Earth, located on average at a distance from the Sun, receives solar radiation power per unit area equal to .

We neglect the absorption of solar radiation by the atmosphere.

## Question

Indicate how varies the power received per unit area with the distance from the source to the receiver and literally calculate the total power emitted by the Sun in the form of electromagnetic radiation.

### Hint

### Solution

The radiation emitted by the Sun being isotropic, the power emitted by the Sun is also distributed over a sphere centered on the Sun and radius .

Therefore, received power per unit area at distance is :

Finally :

## Question

Consider a spherical material particle, perfectly reflecting, center M, with radius and uniform density , located at a distance from the Sun.

The light from the sun reflects on it according to the laws of geometrical optics and it is assumed that all the incident light is reflected in the reverse direction as in the case of a plane mirror at normal incidence.

### Hint

### Solution

A photon of initial momentum :

Restart after reflection on the particle M in the opposite direction by yielding to this momentum :

During the time interval , the light energy received by the particle :

Corresponds to the number of photons :

The impulsion received by the particle during is then :

The average force exerted on the particle is therefore :

The pressure is deduced :