To obtain the caustic curve of the catenary with radiant point O, we start with the catenary locus, and draw in the normals to points on the locus. For each point P on the curve, reflect line OP in the normal at P. The envelope of reflected lines is the caustic.

Click the diagram below to activate the applet, and then click the ‘Animate’ button, or manually drag the red driver point along the x-axis. Both methods give a good representation of the caustic curve. Can you describe this curve?

This caustic curve is not a curve we have studied before. We might describe it as a catenary (parabola?) shaped curve with an internal cusp at the base. It is quite an attractive curve!