Rotating Mirrors
No mysteries with the flat 180° mirror: rotate it and your image stays straight in front of you.
The two mirrors joined at a 90° corner give you the sight-corrected, or ‘tailor’s mirror’, image – you as the rest of world sees you, not right-left reversed.
The two mirrors joined at 60° are at a critical angle: the image you see has been reflected three times, off the first mirror onto the second, off the second back onto the first, and off the first back towards you. That’s 60° three times over: 180°.
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