Cross section - scattering of light by light

[wavingerwin]

Homework Statement

Red and green laser (wavelength of 650 nm and 532 nm respectively) are directed towards each other at 20 degrees.
Each laser has 5 mW power, with diameter of 1mm.

Assuming the intensity of the beams are decreased by 10% each after the 'collision',
estimate the upper limit on the cross section, σ, for the scattering.

Homework Equations

σ = 0.1*(N_RED + N_GREEN) / (N_RED + N_GREEN)*π*0.0005^2

where N is the number of photons per second
N = 5e-3 / (hc/λ)

The Attempt at a Solution

I'm just unsure whether the equation I used for σ is correct or not.
Can somebody confirm?

Many thanks in advance!

 

[mark726]

Thank you for your question. Your attempt at a solution is on the right track. However, there are a few things that could be clarified and some minor corrections that need to be made.

Firstly, the equation you used for σ is not quite correct. The correct equation for the cross section of scattering is σ = (NRED + NGREEN) / (NRED + NGREEN)*π*0.0005^2. This is because the intensity of the beams is already taken into account in the calculation of NRED and NGREEN, so it does not need to be included again in the final calculation of σ.

Also, in your calculation of NRED and NGREEN, you used the power of the lasers (5 mW) instead of the intensity. The intensity is given by I = P/A, where P is the power and A is the area of the beam. In this case, the area of the beam is π*0.0005^2, so the correct calculation for NRED and NGREEN would be NRED = 5e-3 / (hc/650e-9)/π*0.0005^2 and NGREEN = 5e-3 / (hc/532e-9)/π*0.0005^2.

Lastly, the equation you used for σ assumes that the intensity of the beams is decreased by 10% each after the collision. However, the homework statement states that the intensity is decreased by 10% for each beam, not for both beams combined. Therefore, the correct equation for σ would be σ = (0.9*NRED + 0.9*NGREEN) / (NRED + NGREEN)*π*0.0005^2.

I hope this helps clarify your solution. If you have any further questions, please don't hesitate to ask. Keep up the good work!