Twin primary rainbows scattering by a liquid-filled capillary

The twin primary rainbows scattered by a liquid-filled capillary are investigated with Debye theory and geometric optics. From the numerical simulations, a critical radius ratio of the core to the coating of the coated cylinder is proposed to judge the existence of the α and β supernumerary bows. When the ratio is less than or around the critical value, the α and β supernumerary bows disappear. On the premise that the α and β supernumerary bows exist, the β rainbow can always be detected. However, the α supernumerary bows sometimes submerge in the other scattering structure so that the α rainbow cannot be detected under this condition. Four frequency peaks in the angular frequency spectrum of the twin primary rainbows are investigated numerically. Furthermore the relationship between F3 (the third frequency peak which is similar to the ripple frequency of the scattering by a homogeneous cylinder) and the external radius of the capillary is obtained. Experiments are carried out to verify the numerical works with capillary filled with deionized water.