Why Does the Change in Momentum Equal 2pi in Laser Beam Force Calculations?

[Marcin H]

Homework Statement

Homework Equations

F=(del)p/(del)t

The Attempt at a Solution

I understand how to do part a, but on part b I don't understand why the change in momentum is 2pi. I originally did the problem by just subbing (del)p with h/lambda. Why is it 2pi?

 

[jwinter]

If the photon was absorbed then its momentum is simply transferred to the surface but if it is reflected then twice that amount of momentum must be transferred because it both comes to a stop (=absorbed) and then fires away from the surface with the opposite momentum it arrived with.

 

[Marcin H]

If the photon was absorbed then its momentum is simply transferred to the surface but if it is reflected then twice that amount of momentum must be transferred because it both comes to a stop (=absorbed) and then fires away from the surface with the opposite momentum it arrived with.

Ohhhhh ok, that makes sense now. I am confused on part c now. Is part c correct here? It doesn't make sense looking at the units. I don't really see how those units cancel to get you an answer in Newtons. I know I have to use F=(del)p/(del)t, but what is (del) t? It's not given and I'm not sure how to find it. That's how I was trying to do it.

 

[jwinter]

The units are correct. Newtons are just a short and useful name for kg-m/s². Think about the force due to gravity F=ma. There you have force = mass (kg) times acceleration (m/s²).

Δp/Δt is simply the rate of change of momentum with time, or if you like ∂p/∂t or p'(t).

So the force is the rate at which momentum is changing - which in your case is simply
photon arrival rate (N/sec) * momentum transferred by each (kg-m/s) => kg-m/s²