Rainbows by elliptically deformed drops. I. Möbius shift for high-order rainbows

Area of Science:

• Atmospheric optics
• Light scattering
• Rainbow phenomena

Background:

• Rainbows are optical phenomena caused by light scattering in water droplets.
• The shape of water drops, particularly their deviation from spherical, influences rainbow characteristics.

Purpose of the Study:

• To investigate the Möbius shift of rainbow angles for elliptical particles.
• To analyze the impact of drop ellipticity and tilt on rainbow angles.
• To determine how sun angle and drop flattening affect rainbow spacing and insensitivity.

Main Methods:

• Utilized ray theory to derive the Möbius shift for elliptical particles.
• Adapted theoretical results to the geometry of sunlight scattering by falling water drops.
• Analyzed the variation in angular spacing between supernumeraries along the rainbow arc.

Main Results:

• Derived the Möbius shift as a function of ellipse tilt and sun height angle.
• Identified conditions where the rainbow angle is insensitive to drop flattening.
• Demonstrated the dependence of the Möbius shift on drop refractive index for higher-order rainbows.

Conclusions:

• The shape and orientation of water drops significantly influence rainbow characteristics.
• Understanding these effects is crucial for interpreting atmospheric optical phenomena.
• The study provides insights into the physics of rainbows beyond the idealized spherical drop model.