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Physics3, question on intensity, power, wavelength

  1. Feb 19, 2009 #1
    hi folks, here's another problem I've made a few incorrect guesses on. On my other post I may have not mentioned the potential for errors in using various SI units, but I think in general I'm careful enough so I'll continue to not worry about that in this post. So assume I know enough to convert grams to kilograms, and nanometers to meters, etc.

    1. The problem statement, all variables and given/known data
    A scientist wishes to study the behavior of individual photons. To do that, she must decrease the intensity of her i_1 mm2 laser beam -- the laser emits radiation with wavelength w_1 nm -- to a level at which there is no more than one photon in her apparatus at any given time. The path length of the light beam from source to detector is L_1 m. What should be the intensity?

    2. Relevant equations
    for intensity i've used I=P/A, power over area.
    for Power of the laser in terms of the photons, I used P = N * E, where N is the number of photons and E is the energy of a photon. for calculating the energy of a photon I used E = h*c/w_1, where h is Planck's constant, c is the speed of light, and w_1 is the wavelength. so in this problem, P = N*6.6*10^(-34)*(3*10^8))/(w_1*10^(-9)).


    3. The attempt at a solution

    Hmm. I guess I just realized I wasn't sure what to use for A in the equation for intensity. I think in my first guess I just set A=1, without really thinking.

    In my guess I realized I didn't use the distance L_1, which I feel is bad. I wasn't really sure how to incorporate it into the problem.

    So I'm considering the quantity of L_1/c, which might be how long it takes a photon to reach the detector? but I'm not certain of this.

    I'm not getting this right because using my conceptual understanding of the scenario and the equations i have at hand, I don't have a complete cohesive picture.

    Any tips would be appreciated. Thanks.

    ,Yroyathon
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Feb 19, 2009 #2

    Redbelly98

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    I'm guessing that "in her apparatus" means in the L1 m between the source and the apparatus.

    So basically, the beam must contain 1 photon per L1 m of beam length. Can you use that information to say how many photons per second the beam would have?
     
  4. Feb 19, 2009 #3
    exactly. I'm thinking the quantity L_1/c is the number of photons per second the beam would have. the units seem to match up too, and intuitively i think this number should be pretty small, as it is.
     
  5. Feb 19, 2009 #4
    well that did not work out. hmmm. i'll think on it more, trying to understand it conceptually, but as always any suggestions would be great.
     
  6. Feb 19, 2009 #5

    Redbelly98

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    It should have worked out. From L1/c for the number of photons per sec, and also the energy per photon, you can get
    power=energy/sec​
    and from there use the area to get the intensity. Looking at the units will be a good way to check the final answer.
     
  7. Feb 19, 2009 #6

    Redbelly98

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    Aaaack, hold on a minute!

    1/L1 is the number of photons per m.

    c/L1 is the number of photons per second.
     
  8. Feb 19, 2009 #7
    (also, i'm going to rename i_1 as A, which was a misnomer in my head since that figure is not an intensity but an area)

    I got it! it turns out that I had that one figure upside down. the number of photons per second the beam should have is very large actually (my intuition was that it should be small).

    so N=c/L_1 was what worked out.

    So with I=P/A, and P=NE, and E=hc/w_1, and N=c/L_1, i get

    I=P/A=NE/A=(c/L_1)*(h*c/w_1)/A=h*c*c/(L_1*w_1*A)

    Awesome! Thanks for your help!
     
  9. Feb 19, 2009 #8
    exactly!
     
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