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Homework Help: Laser Beam Question

  1. Dec 5, 2007 #1
    1. The problem statement, all variables and given/known data

    If a 20-W laser beam, which has an initial diameter of 2.0 mm, spreads out to a diameter of 2.0 m after traveling 10,000 m, what is the final intensity of the beam?

    A. 20 x 10-4 W/m2
    B. 20 x 10-6 W/m2
    C. 20 x 10-8 W/m2
    D. 6.4 W/m2
    E. 6.4 x 10-6 W/m2

    2. Relevant equations

    I found an equation that states if light hits a surface area A at normal incidence, the intensity I is equal to:

    I = <P> / A

    3. The attempt at a solution

    If I draw this beam out, I have a frustrum of a right circular cone.

    The lateral surface area of a frustrum = PI * S * (R + r) where R and r are the radia and s is the diagonal side.

    After a little math, I found s to be about 10000. It is a little over but its neglible.

    So the surface area would be = PI * 10000 * (.001 m + 1.0 m) = 31447.3 m^2

    Wouldnt that mean the intensity I = 20 W / 31447.3 m^2 = .000636 W / m^2

    Intensity = 6.4 * 10^-4 W / m^2

    Obviously, that is not one of the answers. What am I doing wrong here?

    Any help will be greatly appreciated. Thanks in advance.

    Travis Walters
  2. jcsd
  3. Dec 5, 2007 #2


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    Science Advisor
    Gold Member

    Think of it this way. How much energy (watts) do you have through a 2m diam. circle?
  4. Dec 5, 2007 #3
    Hey there,

    For reference, the answer key says 6.4 W/m2 is the correct answer.

    The answer I got was 6.4 * 10^-4 W / m^2, so I am just wondering the answer is a typo.

    I am not sure where you are getting at dlgoff? Please explain :)

    Thanks in advance.

    Travis Walters
  5. Dec 6, 2007 #4


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    Science Advisor
    Gold Member

    Watts/area. 20W/(3.14xr^2) where r is the radius (1meter).
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