圆形截面微通道的双一阶彩虹现象研究

基于几何光学理论及Debye理论，研究圆形截面微通道这一双层圆柱产生的双一阶彩虹现象。由于全反射现象，双一阶彩虹并非始终存在，故通过数值模拟，得出内外径比的临界值来判断双一阶彩虹的存在性。当双一阶彩虹存在时，双一阶彩虹中的彩虹总是可被观察到；彩虹在某些情况下会因光强较弱而被淹没在以二阶彩虹为主的其他散射结构中。研究发现彩虹位于二阶彩虹主峰右侧时，其可被观测到。为此分析彩虹与二阶彩虹两者主峰散射角重叠这一临界情况，进而提出判断彩虹能否被被观测到的方法。最后，构建实验系统，以充满去离子水的高硼硅玻璃毛细管为对象进行实验研究，通过CCD相机拍摄彩虹图像。结果表明，毛细管内径为550 m、外径为600 m时，其内外径比大于上述临界值0.7485，故双一阶彩虹存在。但是由上述判断方法得出彩虹无法被观测到，这一结论与仅能从拍摄图像中获得彩虹结构的现象相符。

Twin primary rainbows scattered by micro-channel with circular cross-section

The twin primary rainbows scattered by a liquid-filled micro-channel with circular cross-section were investigated with Debye theory and geometric optics. The twin primary rainbows do not always exist because of the total reflection. Therefore with numerical simulation, a critical radius ratio of the core to the coating was proposed to judge the existence of the twin primary rainbows. On the premise that the and rainbows exist, the rainbow can always be detected. However, the a rainbows sometimes cannot be detected when submerging in the other scattering structure. It is observed that the rainbow can be detected only when it locates at the right side of the secondary rainbow. And therefore the situation that the locations of the peaks of second-order rainbow and rainbow coincide was analyzed. Then a judgment criterion for whether the rainbow can be detected was proposed. Also an experiment system was built and a borosilicate capillary filled with deionized water was taken for experiment research. When the internal radius of the cylinder is 550 m and the external radius of the cylinder is 600 m, the twin primary rainbows exist due to the radius ratio is larger than the critical value 0.7485. But the rainbow cannot be observed according to the proposed judgment method. It accords with the phenomenon in the captured pattern that only therainbow can be seen.