Circular Aperture Diffraction, Angle of First Minimum

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1. May 27, 2015

CoffeeCrow

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. May 27, 2015

BvU

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 !

3. May 29, 2015

CoffeeCrow

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.

4. May 29, 2015

haruspex

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.