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Homework Help: Please help me in this light problem

  1. Mar 4, 2005 #1
    Please help me in this light problem!!!

    HI!

    well would u please help me in solving this problem the peoblem is:

    "a laser beam of diameter 1cm is pointed on the moon. what is the diameter of the area illuminated on the moon. The moon is about 240000 miles away. take wavlength=6328A."

    The solution that im using is this.

    tan (lambda/2d)=x/2/R ; (R is the distance between the moon and the slit)

    since lamda<<d

    therefore tan (lambda/2d)=lambda/2d

    so we now have:

    lambda/2d=x/2R
    or x=lamda(R)/d

    where x is the required answer.

    Now tell me that that is this the right method to get the required answer?

    if not then what is the right method?

    secondly can u explain how we can take angle as lamda/2d

    Thanks in advance
     
  2. jcsd
  3. Mar 4, 2005 #2

    xanthym

    User Avatar
    Science Advisor

    The laser is diffracted by its CIRCULAR aperture, which has different properties than single-slit diffraction. Fraunhofer diffraction applies in the far-field for our case:
    {Angular Displacement of First Minimum} = θ1 :SUCH THAT: sin(θ1) = (1.22)λ/d
    where "d" is laser's circular aperture diameter. In the far field:
    {Radius of First Minimum on Target} = r = D*sin(θ1)
    where D is target distance. From the first equation above and using {D = 240000 mi = 386e(6) meter}, {λ = 6328e(-10) m}, {d = 1.0e(-2) m}:
    r = D*(1.22)λ/d = {386e(6) m}*(1.22)*(6328e(-10) m)/(1.0e(-2) m) = (29,800 m)
    {Laser Spot Diameter On Moon} = 2*r = (59,600 meters)


    ~~
     
    Last edited: Mar 4, 2005
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