Butterfly Waves & Caustics ~ Images by Fausto Lubatti.  The flapping of a single butterfly’s wings in Japan may or may not trigger a tornado in Texas but here a single butterfly landing on a small pond in the Italian Alps has set off beautiful optical effects.

Images ©Fausto Lubatti. Shown with permission

The tiny butterfly has landed on the water surface at top right creating a set of outgoing concentric water waves.

The more obvious bright circles centred near the image middle are not waves, they are bright line caustics on the pond bed and produced by refraction at the wavy water surface.  

The spectral colours are the images of the caustics refracted and dispersed into individual wavelengths as they emerge at the wavy and sometimes severely sloping water surface.    Here the refraction effect is marked and, thanks to the butterfly, well ordered.   The same effect can sometimes be seen in a shallow sea as intense flashes of coloured light.

Caustics are Nature’s ‘focusing’.   Unlike images from our lenses, caustics are always sharp. They mark spatial discontinuities in light ray behaviour.     The butterfly waved pond surface refracts sun rays.   Regions where the surface is convex deflect rays to form volumes where pairs of rays cross.   At the volume edges the ray crossings cluster and there is a corresponding concentration of light – a caustic surface.   Elsewhere there are no rays crossing.   The caustic surface is at the boundary of two spaces where pairs of rays cross or do not cross at all.

The intersection of the caustic surfaces with the pond bed gives the bright circles seen at the upper picture’s centre and at lower left.  

The colours result when the white caustic is viewed through a sharply tilted wave surface and the white is dispersed into spectral colours.

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The bright circles are on the pond bed. They are the intersections of caustic sheets with the bed.