If you are looking for a derivatation which starts at a more fundamental level than that, then you should pick up any textbook on lasers. Any textbook you can find will cover the derivation of the Gaussian modes of a laser beam from the wave/Helmholtz equation. You can also look at section 2.1 of my thesis where I sketch out the derivation from the Helmholtz equation although I stop slightly short of deriving the divergence angle.

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The diaphragm, a dome-shaped muscle at the base of the lungs, plays an important role in breathing — though you may not be aware of it. When you inhale, your diaphragm contracts (tightens) and moves downward. This creates more space in your chest cavity, allowing the lungs to expand. When you exhale, the opposite happens — your diaphragm relaxes and moves upward in the chest cavity.

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You can also practice this sitting in a chair, with your knees bent and your shoulders, head, and neck relaxed. Practice for five to 10 minutes, several times a day if possible.

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But it's especially important for people with chronic obstructive pulmonary disease (COPD). In COPD, air can become trapped in the lungs, which keeps the diaphragm pressed down. This causes it to weaken and work less efficiently. Diaphragmatic breathing can help people with COPD strengthen the diaphragm, which in turn helps them use less effort and energy to breathe.

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I will assume that you are asking about laser beams in the fundamental, diffraction limited Gaussian mode. The standard expression for the divergence angle of a Gaussian beam in the far field is (see the Wikipedia page on Gaussian beams) $$ \theta=\frac{\lambda}{\pi\omega_0} $$ where $\omega_0$ is the so-called waist size of the Gaussian beam. From here you can calculate the solid angle subtended by the beam which is given, in the small $\theta$ limit, as $$ \Theta\simeq\pi\theta^2=\frac{\lambda^2}{\pi\omega_0^2}=\frac{\lambda^2}{A}, $$ where $A$ is the area of the beam's waist.

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Laser divergence angleformula

Relearning how to breathe from the diaphragm is beneficial for everyone. Diaphragmatic breathing (also called "abdominal breathing" or "belly breathing") encourages full oxygen exchange — that is, the beneficial trade of incoming oxygen for outgoing carbon dioxide. Not surprisingly, this type of breathing slows the heartbeat and can lower or stabilize blood pressure.

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All of us are born with the knowledge of how to fully engage the diaphragm to take deep, refreshing breaths. As we get older, however, we get out of the habit. Everything from the stresses of everyday life to the practice of "sucking in" the stomach for a trimmer waistline encourages us to gradually shift to shallower, less satisfying "chest breathing."