The BSS sundial glossary has the following entry under "Types of Dials":

"reflecting ~: these dials have no gnomon, but reflect sunlight by means
of a semi-cylindrical mirror, set with the axis of the mirror parallel
to the polar axis. The mirror reflects the light to form a caustic curve
amongst the hour points. For the special case of the mirror having a
cycloid shape, the hour points are equally spaced. Note that the term
reflecting dial may also be used for ceiling dials."

What is the typical dialface for a 'reflecting dial'?  Are the comments
above about semi-cylindrical mirrors apply equally to ceiling and wall
dials?

If a polar ceiling dial has an inclination of phi/2 what does having a
mirror inclined at phi do?

What is a caustic curve?

David

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