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Power of laser beam to support a reflecting aluminum foil?
A laser beam shines vertically upward. What laser power is necessary for this beam to support a flat piece of aluminum foil with mass 32 micro g and diameter equal to that of the beam? Assume the foil reflects all the light.
Let E be the energy per photon and f be the number of photons per second. Then Ef would be the power of the beam.
Now E=mc^2 and momentum = mc so momentum = E/c
Impulse = momentum
Impulse = force x time
frequency = 1/time
Impulse x frequency = force x time / time
Impulse x frequency = force.
Substitute E/c for Impulse and f for frequency
E/c x f = force
The direction of the photons reverses direction so the change in momentum is double the original momentum.
The total force is 2Ef / c or 2 Power / c
Solve for the weight of the foil assuming g = 9.8m/s^2
Then solve for Power assuming c = 3e8 M/s
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