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Critical angle light scattering from bubbles: an asymptotic series approximation
Abstract:
The critical scattering angle at 82.8 degrees from an air bubble in water locates the transition from partial to total re-flection from elementary geometrical optics. The irradiance scattered into a narrow angular region near the critical scattering is a monotonically increasing function of bubble radius a provided a >> lambda, and the weak contributions from rays reflected internally from the far side of the bubble are neglected. The asymptotic series for critical angle scattering derived here leads to a simple approximation for the irradiance. It also describes the breakdown of elementary geometrical optics for reflection at the critical angle from a curved surface. The leading correction to the scattering amplitude relative to the perfect reflection amplitude is found to be O(beta(-(1/4))), where beta = 2pia/lambda is the size parameter and lambda is the wavelength of light in water. The series is confirmed by comparison (as a function of beta) with smoothed Mie computations. The leading correction is significant for beta as large as 20,000, and it is larger when the light is polarized with the E field parallel to the scattering plane rather than perpendicular to it. The dependence on beta(-(1/4)) is also shown from an average of the reflection coefficient over a Fresnel zone. Applications to optical bubble sizing are noted, and the nature of approximations in previous physical-optics models of critical angle scattering is clarified.
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Accuracy, limits, and approximation
Accuracy is defined as the closeness of the measured value to the true or actual value. In engineering mechanics, repeated measurements are taken during theoretical or experimental analyses to ensure that the result is precise and accurate.
The accuracy of any solution is based on the...

