Question about the force from a photon on a mirror

[sharkybait]

Homework Statement

My homework question is: A flashlight beam produces 2.5W of electromagnetic radiation in a narrow beam. Although the light it produces is white ( all visible wavelengths), make the simplifying assumption that the wavelength is 550 nm, the middle of the spectrum. What force would the beam exert on a perfect mirror ( reflects light completely)?

Homework Equations

E=hc/wavelength
Force=momentum/Time
Power=Energy/Time
E=pc

The Attempt at a Solution

We need to find the force so I decided the best way to go about this is to use the relationship F=Momentum/Time.

1. E=hc/wavlength used to find the momentum P=E/C.
2. Once I found the momentum I used the relationship Power=Energy/Time and then solved for Time yielding Time = Energy/Power.

3.Now that I had both the Momentum and Time I simply solved the equation F=momentum/time.


The answer I am supposed to get is 1.67*10^-8 N while the answer I got was 8.36*10^-9 N. The correct answer turns out to be exactly two times the answer I calculated. Could anyone give me some insight into why this is the case? I think there is some conceptual aspect to this problem I may be missing. Thanks for any help.

 

[joeghal87]

Hello there,

here is the explanation :

what you did is absolutely correct, except for the Force formula.

The force is the change of momentum per unit of time and not the value of the momentum per time. So its F = dp/dt and not F = p/t

Therefore, the conceptual aspect that you missed in the problem is "the perfect mirror" (reflects light completely). The force needs to be twice the momentum/time value because the flashlight beam is totally reflected when it hits the mirror (100% reflexion)

The force formula should be then : F = 2p/t which explains why the correct answer is exactly twice the one you obtained

 

[sharkybait]

Hello there,

here is the explanation :

what you did is absolutely correct, except for the Force formula.

The force is the change of momentum per unit of time and not the value of the momentum per time. So its F = dp/dt and not F = p/t

Therefore, the conceptual aspect that you missed in the problem is "the perfect mirror" (reflects light completely). The force needs to be twice the momentum/time value because the flashlight beam is totally reflected when it hits the mirror (100% reflexion)

The force formula should be then : F = 2p/t which explains why the correct answer is exactly twice the one you obtained

Thanks for the help!