We next ask: what is the caustic curve of the nephroid relative to its centre? At each point P of the nephroid locus we draw the normal to the curve. Now take the reflection of OP in this normal, and the caustic curve occurs as the envelope of these reflected lines.

Click the diagram below to activate the applet, and then click the ‘Animate’ button to generate the pedal curve. Clicking the little red x at bottom right will clear the drawing from the applet window. Now drag the red point Q slowly along the segment. Can you describe the construction? Describe the resulting caustic curve.