Consider two balls that look identical and have the same mass but that are made from completely different materials. The "happy" ball is very bouncy; the "sad" ball absorbs energy. The two balls will be rolled, one at a time, down a ramp toward a block of wood. Which ball knocks the block over?

1. the happy ball
2. the sad ball
3. the balls have the same momentum when they reach the block so they have an equal chance of knocking the block over

The sad ball stops when it collides with an object, experiencing a momentum change of -mv. The momentum of the bouncy ball changes from +mv to -mv, a change of -2mv, transferring twice as much momentum. The same thing happens with light - light reflecting from an object transfers twice as much momentum as light absorbed by an object.

For an EM wave there is no mass associated with the wave and yet the wave has momentum. When the wave is absorbed or reflected by an object, momentum is transferred to the object.

The momentum of an electromagnetic wave is its energy divided by its speed.

p

=

U c

A perfect reflector acquires a momentum of

Dp

=

2U c

For a perfect absorber

Dp

=

U c

The energy depends on time, so let's define something that does not depend on time. We can define a radiation pressure, P.

For the reflector

P

=

2I c

For the absorber

P

=

I c

(this is equal to the energy density, u).

People have proposed using radiation pressure to propel a spacecraft. If the spacecraft has large reflecting sails (solar sails), radiation pressure from sunlight can be used to accelerate it, although it can only accelerate away from the Sun.