Bubble optics: upward emerging ray paths.

Light scattered by floating bubbles is a fascinating everyday phenomenon and a relevant issue for climate science and remote sensing. Here, we discuss light scattering in the upward hemisphere in the geometrical optics (GO) approximation for plane wave incidence with various inclinations on isolated floating bubbles of various sizes, using numerical and analytical caustic theory methods. We identify and discuss the relevant ray paths and explain the caustic evolution observed on a screen placed close to and above a large bubble.

Bubble optics: Leonardo's cross revisited-Part 3, nonparaxial analytical methods.

In about 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the circularly symmetric meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in two companion papers using a numerical ray theory spot diagram approach, and paraxial analytical methods. In this study we employ nonparaxial analytical methods, which are necessary when the outer bubble meniscus rises high above the ambient water surface.

Bubble optics: Leonardo's cross revisited-Part 2, paraxial analytical methods.

Around 1508, Leonardo da Vinci first noted and sketched a cross-shaped caustic produced by a plane wave diagonally incident on the meniscus surrounding a bubble on the surface of a water-filled container. This caustic was analyzed in a companion paper using a numerical ray theory spot diagram approach and is analyzed here using analytic ray theory approaches appropriate to the paraxial regime. We demonstrate that the caustic assumes the standard astroid form when the maximum meniscus slope is small, and the shape starts to distort as the maximum meniscus slope increases.

Bubble optics: Leonardo's cross revisited-Part 1, numerical methods.

Around 1508, Leonardo DaVinci observed a curious image of the sun formed by a floating bubble. Now, some 500 years later, we give a full picture of the surprisingly rich phenomenology of the light pattern formed below surface bubbles. Under shallow illumination, and for shallow depths of water, the caustic deviates from the symmetrical astroid shape obtained for larger depths and/or near-vertical illumination.

Optical caustics of multiple objects in water: two vertical rods and normally incident light.

The optical caustics of the combined water menisci raised by two objects with identical circular cross sections show peculiar caustic metamorphoses known from binary gravitational lenses. We highlight their genericity and analyze the connection of the refracting interface topography and curvature landscape with the caustics' (and their images') topology.