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Force exerted by a laser beam

  1. Jul 27, 2007 #1
    1. The problem statement, all variables and given/known data

    A laser beam ([tex]\mathrm{Power} = 1\ \mathrm{W})[/tex] is completely reflected by a mirror perpendicular to the beam. Light is made of photons, and each photon carries an energy [tex]E = h\nu[/tex] and a momentum [tex]P = h/\lambda[/tex], where [tex]\nu[/tex] is the frequency, [tex]\lambda[/tex] is the wavelength and [tex]h[/tex] is Planck's constant. Find the force with which light pushes the mirror.

    2. Relevant equations
    Apart from those already present in the problem statement, I have:
    [tex]\lambda \nu = c[/tex]

    [tex]F = \frac{dp}{dt}[/tex]

    3. The attempt at a solution
    Each second, the light source emits [tex]n[/tex] photons, each one carries an energy [tex]E = h\nu = hc/\lambda[/tex], for a total power of [tex]1\ \mathrm{W}[/tex]. This gives:

    [tex]\displaystyle n = \frac P E = \frac{\lambda}{hc}[/tex]

    In one second then, [tex]n[/tex] photons hit the mirror and bounce back, which gives:

    [tex]\displaystyle F = \frac{dp}{dt} = n \cdot 2p = 2 \frac{\lambda}{hc}\cdot \frac{h}{\lambda} = \frac 2 c \approx 6.67\cdot 10^{-9}\ \mathrm{N}[/tex]

    The result is somewhat intuitively pleasing, can you check it is correct, please?
  2. jcsd
  3. Jul 27, 2007 #2

    Doc Al

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    Staff: Mentor

    Looks good to me.
  4. Jul 27, 2007 #3
    Whew... Thank you Doc for checking :)
  5. Feb 21, 2009 #4
    Sorry to dig up such an old question, but after looking at this question, I don't understand were the 2 comes from in the F=n2p. Could someone explain this to me?
  6. Feb 21, 2009 #5


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    The momentum is twice the incoming photon's because it bounces back
    Think of a ball, if you throw it to hit a wall and stop then you need twice as much force for it to hit the wall and come back at the same speed.
  7. Feb 21, 2009 #6
    That is to say, if it was not a mirror, and the light did not reflect off the surface, the 2 would be a 1 instead?
  8. Feb 21, 2009 #7

    Doc Al

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    It comes from the fact that the change in momentum is twice the original momentum.
  9. Feb 21, 2009 #8


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    Yes. If the light is absorbed then it's a 1. As Doc Al said, it's all about change in momentum.
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