Optical behavior of surface bubbles

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. Whereas the astroid caustic involves refraction through the outer meniscus only, more complex ray paths explain the asymmetric, multicomponent (composite) light pattern.

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Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods

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Selmke

2021

Appl. Opt.

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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. We show that competition between generalized coma and generalized astigmatism, with generalized coma dominating, is responsible for the cusp points of the astroid in the plane of the incident light being reversed with respect to their images in the exit plane of the optical system. We also show that Leonardo’s cross is the result of the twofold symmetry of the astigmatic focusing of the diagonally incident plane wave by the circularly symmetric meniscus.

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Optical behavior of surface bubbles

Cited by 4 publications

References 21 publications

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

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

Bubble optics: Leonardo’s cross revisited—Part 1, numerical methods

Bubble optics: Leonardo’s cross revisited—Part 2, paraxial analytical methods

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