Caustics & Lenses

Two glasses, at right a smooth lead crystal and at left a soda glass.

The higher temperature softening point soda glass has an uneven cross section that adds to its charm. The irregularities refract the rays of the late afternoon sun to produce bright caustic patterns on the wall. The patterns are those dancing on stream beds, in shallow seas and in swimming pools and twinkling stars but here they are frozen, immobile.

Images by Mario Frietas (site) of Universidade Tecnológica Federal do Paraná, Brazil.

All images ©Mario Frietas, shown with permission

A lens produces a sharp focus at only one point in space (or along a line if cylindrical).

Elsewhere there is a blur.

Caustics versus Lenses

Caustics are surfaces in space where rays cross one another and cluster and coalesce together to give a high light intensity. In classical physics the intensity would be infinite but wave diffraction avoids this embarrassment.

Mathematically a caustic is more, it is a spatial discontinuity and rays behave differently on each side of the surface or sheet. Catastrophe theory has much to say about the structure and order of caustics that we sense in the shifting patterns on a stream bed, a boat hull or swimming pool floor.

Where the caustic surface reaches a solid surface we see a sharp bright line. It is always sharp wherever the caustic sheet is made visible.

In comparison our carefully crafted lenses are poor things. At best they focus rays at only a single point (or line) in space. Move away from the focus and there is an increasing blur.

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A caustic sheet is a surface where rays cross and cluster most densely.

Its intersection with a solid surface produces a bright line.

The line is always sharp