Critical angle scattering by a bubble: physical-optics approximation and observations

The intensity of light scattered by an air bubble in water is predicted by the geometric-optics calculation of Davis (1955) to have a divergent angular derivative as the critical scattering angle ϕc is approached. Effects of diffraction in the angular region near ϕc are described here. The Fraunhofer diffraction for scattering angles ϕ≤ϕc is estimated using a simplified physical-optics approximation. A ringing and decay of the far-field intensity is predicted that is formally similar to the near-field diffraction of a straight edge. Observation of millimeter radius bubbles in water with collimated monochromatic illumination confirm the existence of this ringing which has a quasi period ≃ 25 mrad. The diffraction calculation gives an approximate description of the relative ϕ of the observed maxima and minima. Fringes with a lower contrast and spacing ≃ 0.3 mrad were also observed; they appear to be caused by the interference of rays with distinct paths. Implications for the critical angle scattering of white light are discussed.