The _divergence angle_ is the degree to which a beam's radius increases as it propagates in the [far-field limit.](Far-field%20propagation.md) For a [Gaussian beam](Gaussian%20beam.md) it is defined as $\Theta = \frac{2\lambda}{\pi w_0}$ where often the divergence beam half angle is given instead such that $\theta=\frac{\lambda}{\pi w_0}.$ ^11f1c0 The half divergence angle for a Gaussian beam is shown below.  # Derivation of the divergence angle The divergence angle is derived from linearizing the [Gaussian beam radius](Gaussian%20beam%20radius.md) such that  becomes   # Beam parameter product  %%See Fowles pg 466%% #Electromagnetism/Optics/waveOptics/GaussianBeamOptics