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 Φ<sub><i>c</i></sub> is approached. Effects of diffraction in the angular region near Φ<sub><i>c</i></sub> are described here. The Fraunhofer diffraction for scattering angles Φ≤Φ<sub><i>c</i></sub> 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 theobserved 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.
© 1979 Optical Society of America
Philip L. Marston, "Critical angle scattering by a bubble: physical-optics approximation and observations," J. Opt. Soc. Am. 69, 1205-1211 (1979)