= Corner reflector
{wiki}
Three mutually perpendicular mirrors reverse a ray's direction when it encounters all three. With <orthonormal> normals $a,b,c$, write the reflections as $I-2P_a$, $I-2P_b$, $I-2P_c$. Their <orthogonal projection matrices> have pairwise products zero and sum to $I$ by the <resolution of the identity in an orthonormal basis>. The product of the three reflections is therefore $-I$. It reverses every incident direction independently of the order in which the mirrors are met. Real apertures restrict which incoming rays actually reach all three reflecting faces. Such <retroreflectors> provide the returning-light geometry in <lunar laser ranging>.
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