Momentum and radiation pressure

MOMENTUM AND RADIATION PRESSURE

It is important to note that as EM waves carry energy, they also carry momentum. Maxwell proved that wave energy U and momentum are related by

where v is energy density and c is the velocity of light.

As the electromagnetic waves carry momentum, they exert pressure when they are reflected or absorbed at the surface of a body. This is known as radiation pressure.

From Newton's second law, the change in momentum is related to a force by 

then for a flat surface of area A, which is perpendicular to the path of an EM wave radiation, the energy intercepted in a given time Δt is

So, from eqn. (1), the momentum is

This is the relation for the total absorption of EM radiation.

This is due to 'ΔP', the momentum change and the direction of momentum change of the object is the direction of the incident EM radiation that the object absorbs.

If the radiation is completely reflected back by the object along the original path then

Thus if the radiation is partly absorbed or completely reflected by the object, the magnitude of the force on area A varies between the values

Radiation pressure

The force per unit area on an object due to EM radiation is the radiation pressure Pr. Thus from eqns. (5) and (6) we obtain

for total absorption of radiation and

for total reflection back along the path