The momentum added to an object by light energy (E) shining on it (eg solar sails) is E/C. Why?

Question

My physics is only up to A-Level, so I'm probably wrongly mixing Newtonian physics with photons...

Can someone explain a simple derivation?

For kinetic energy:
E = 1/2 x m v^2

So I wondered why mv [momentum] does not equal 2E/c (kinetic energy equation) when it's applied to photons.

Answer 1

p = mv = (E/c^2) * c = E/c

Answer 2

You're right about being wrong, photon don't follow Newton's laws.

A photon sail isn't like a traditional sail, where the air particles bounce off the sail and directly transmit their kinetic energy.

Photons are absorbed into atoms, and are consumed by exciting electrons. I don't fully understand the process myself, but having excited electrons makes you move. I think they transmit some other sort of energy when they relax to ground state.

Answer 3

The equations you have quoted are classical equations which do not account for relativistic (fast moving) effects. They are a simplification of the relativistic equations. At slow (everyday) speeds, the relativistic equations reduce to the formulas above. At fast moving speeds, like a photon at the speed of light, the relativistic effect becomes the dominant part of the equation.
See the wikipedia entry for relativistic mass for further understanding.

Answer 4

Sorry matey, no idea, but it looks really intelligent! Keep up the good work.