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?

Solutions of Savchenko Problems in Physics

Aliaksandr Melnichenka
October 2023

    <h3 id="back-link"><a href="/#1.1">$\leftarrow$Back</a></h3>

    <h3> Statement </h3>
    <p>
        $1.1.21.$ 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?

    <h3>Solution</h3>
    <p>
        

$a)$ 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:

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

    <h4>Answer</h4>
    <p>
        $$(-c_x,c_y,c_z), (-c_x,-c_y,-c_z)$$
    </p>


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