2. What is the radiation pressure (force/area) of a laser pointer on a heavy, hi

Question

2. What is the radiation pressure (force/area) of a laser pointer on a heavy, highly absorbing surface? Assume that the laser has an output power of 1mW, a wavelength of 600nm, and a beam radius of 1mm. To do this problem, first compute the number of photons per unit time in the beam seen by the absorbing surface. Then compute the momentum transfer that occurs at the surface when a photon is absorbed. Finally, take the pressure to be the total momentum transfer per unit time per unit area. Write your answer in terms of Newtons of force per square meter of area (which is called a

Explanation / Answer

energy of a photon is h nu nu = c/lamda (frequency is speed of light over wavelength) Physics greeting "What's new?" Geeky answer, "c over lamda" c/lamda = 3 x 10^8 /600 x 10^-9 energy of photon = h c / lamda = 6.63 x 10^-34 Js(5.0 x 10^14/s) = 1.33 x 10^-48J 1mW is 0.001J/s number of photons per second = 0.001J/1.33 x 10^-48J = 7.54 x 10^44 Momentum transfer is momentum transfered by each photon times the number of photons momentum for absorbed light equals energy/c p = U/c = 1.33 x 10^-48J/3 x 10^8 = 4.42 x 10^-57 kg m/s total momentum = p per photon times photons = 4.42 x 10^-57 kg m/s * 7.54 x 10^44 tot momentum = 3.33 x 10^-12 kg m/s we get this each second so multiply by 1/s pressure is momentum/area area is Pi r^2 = Pi(0.001m)^2 pressure = 3.33 x 10^-12 kg m/s^2/{Pi (0.001m)^2} = 1.06 x 10^-6 N/m^2 pressure = 1.06 x 10^-6 pascals this is about 1 x 10^-11 of atmospheric pressure (divided by 100000) Now we increase by a big factor, let's compare them 1 mW with 1mm radius is 318.3 W/m^2 1015W/ cm^2 = 10,150,000W/m^2 so, 31,900 times more so the bigger laser has a radiation pressure of 0.0338N/m^2 = 0.0338 Pascals Note: converting to photons and back was fun, but 1 mW/speed of light is already the total momentum 0.001W/3 x 10^8 m/s = = 3.33 x 10^-12 kg m/s

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