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Circular Aperture Diffraction, Angle of First Minimum

  1. May 27, 2015 #1
    1. The problem statement, all variables and given/known data

    A helium-neon laser ( ##\lambda =633nm##), is built with a glass tube of inside diameter 1.0mm. One mirror is partially transmitting to allow laser light out. From an optical perspective, the laser beam is a light wave that diffracts through a 1.0mm diameter circular opening. The angle to the first minimum, ##\theta_1## is known as the divergence angle of the laser, find this angle.

    2. Relevant equations

    $$sin(\theta)=1.22\frac {\lambda} {d}$$ Where d is the diameter of the circular opening, and ##\theta## is the angle to the first minimum.

    3. The attempt at a solution


    The light from the laser, as mentioned in the problem statement, is essentially diffracting through a circular aperture of 1.0mm diameter, thus finding ##\theta_1## should be a simple implementation of the above formula:

    $$sin(\theta)=1.22 \frac {633 \times {10^{-9}}} {10^{-3}}$$
    $$sin(\theta)=0.00077\ radians$$
    $$sin(\theta)=0.044\ degrees$$
    $$\theta=0.044\ degrees$$

    Apparently though, the correct answer is ##\theta=0.029\ degrees## and I'm just not sure what I'm missing, any help would be greatly appreciated.
     
  2. jcsd
  3. May 27, 2015 #2

    BvU

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    Clear and complete post. I fully agree with your answer. So does hyperphysics' calculator (here).
    If all of us are wrong, I sure would like to know why and how ! :smile:
     
  4. May 29, 2015 #3
    Thank you! I've spent about an hour and a half on this and I was almost completely sure the solutions were in error, so thanks for confirming that, I really appreciate your help.
     
  5. May 29, 2015 #4

    haruspex

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    Maybe you need to take into account that the beam emerges through glass. A refractive index of 1.5 happens to match the ratio between the two answers.
     
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