# A conceptual question about the force of light waves when reflected

1. Apr 17, 2012

### RubberBandit

1. The problem statement, all variables and given/known data An EM wave with intensity=200 W/m^2 is normal to a black .2m x .3m card that absorbs 100% of the wave. (a) Find the force exerted on the card by the radiation. (b) Find the force exerted by the same wave if the card reflects 100% of the light.

2. Relevant equations
Pr=I/c Pressure=F/A

3. The attempt at a solution
Part (a) I solved. (I/c)(0.2*0.3)=F=4*10^-8 N
Part (b) I know is double the force.

My question is conceptual. Why is the force doubled when the EM wave is reflected?

Thank you for any and all replies.

2. Apr 17, 2012

### Steely Dan

Think about it in terms of momentum. Force is what is required to change momentum; a net change in momentum due to a force is usually called an impulse. In the case of absorption, you only need the card to provide an impulse equal in magnitude to the momentum, which is opposite in direction to the light wave. This will exactly stop the wave. On the other hand, if you want to reflect the wave, you need to not only bring its velocity to zero but then to send it back in the opposite direction at the incoming speed. In other words you need to impart an impulse twice as large because the magnitude of the change in momentum is twice as large.

3. Apr 18, 2012

### RubberBandit

That makes perfect sense. Thank you Steely Dan.

PS Love your handle. Get along Kid Charlemagne.