Thanks, Fer. Apologies all round, and especially to Anselmo.  I now think his proposal would work after all.  But only in the winter months.  At noon at the equinox the reflected beam would be vertically above the mirror.  During the summer months the beam would be reflected south of the east-west line, i.e. back through the window.
Or am I wrong again?
John Lynes
 
Fer de Vries wrote -
The idea by Anselmo is correct.
 
The mirror is just between the polar axis and the horizontal ceilng and by this the pattern on the ceiling looks like a polar dial.
 

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