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.