Droplet Caustics

A host of droplets, each with its caustic tail, imaged by Andrew Kirk. "When I pulled my breakfast out of the microwave oven, there was a lovely pattern of small droplets on the plastic container lid."    ©Andrew Kirk.
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Rays cross inside the caustic surface, they do not cross outside.

The sun had not been up long and was glancing along the plastic lid.   The bright droplet ‘tails’ are along the surface.  

Each droplet focusses sunlight to form a tail.   But round drops are by no means perfect lenses.  Rays passing near the droplet centre are brought to a focus further away than those passing a long way off centre.  This is spherical aberration, the defect that afflicted the Hubble Space Telescope.

The differently focussed rays form a caustic surface rather than a point.  The bright ‘tails’ are where the caustic surface intersects the plastic lid.     The accurate computer ray tracings at left and below show what is happening.   Inside the caustic surface rays cross each other, outside they do not.   The boundary of two such spatially different regions is always a caustic where rays cluster to form a very bright sheet of light.

The heiligenshein, the glow around the shadow of your head on dew wet grass, is produced by these caustics.    The caustic falls onto a nearby leaf surfaces which in turn scatters light back through the droplet.