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Statement

$1.1.21.$ An angular reflector mounted on the moon rover consists of three mutually perpendicular mirrors. If light, whose velocity $c = (c_x,c_y,c_z)$ falls on the reflector. What components will have the velocity of light after reflection from the mirror located in the $yOz$ plane? After reflection from all three mirrors?

Solution

$a)$ Since the mirror in the $yOz$ plane reflects the beam along the $Ox$ axis, the $x$ coordinate is inverted.

Thus, if $\vec{c_1}$ is the reflected ray from $\vec{c}$,

$\vec{c_1} = (-c_x, c_y, c_z)$

$b)$ Similarly, the mirrors in the $yOx$ and $xOz$ planes reflect the beam along the $Oz$ and $Oy$ axes, respectively:

$\vec{c_2} = (c_x, c_y, -c_z)$, for$yOx$

$\vec{c_3} = (c_x, -c_y, c_z)$, for $xOz$

At reflection from three mirrors at once, all components of $\vec{c}$ will take their negative values:

$\vec{c_4} = (-c_x, -c_y, -c_z)$

Answer

$$(-c_x,c_y,c_z), (-c_x,-c_y,-c_z)$$