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<meta name="description" content="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?">
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<meta property="og:description" content="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?">
<title>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?</title>
$1.1.21.$ 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?
</p>
<center>
<figure>
<img src="statement.png"
loading="lazy" width="230" />
<figcaption>
For problem $1.1.21$
</figcaption>
</figure>
</center>
<p>
</p>
<h3>Solution</h3>
<p>
<p>
$a)$ Since the mirror in the $yOz$ plane reflects the beam along the $Ox$ axis, the $x$ coordinate is inverted.
</p>
<p>
Thus, if $\vec{c_1}$ is the reflected ray from $\vec{c}$,
</p>
<p style="text-align: center;">
$\vec{c_1} = (-c_x, c_y, c_z)$
</p>
<p>
$b)$ Similarly, the mirrors in the $yOx$ and $xOz$ planes reflect the beam along the $Oz$ and $Oy$ axes, respectively:
</p>
<p style="text-align: center;">
$\vec{c_2} = (c_x, c_y, -c_z)$, for$yOx$
</p>
<p style="text-align: center;">
$\vec{c_3} = (c_x, -c_y, c_z)$, for $xOz$
</p>
<p>
At reflection from three mirrors at once, all components of $\vec{c}$ will take their negative values:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<meta name="keywords" content="Savchenko Problems in Physics, Savchenko solutions, physics problems, physics olympiad preparation, IPhO, Jaan Kalda">
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<meta name="description" content="The largest dataset of solutions of 'Savchenko. Problems in Physics'. Savchenko’s Problems in General Physics is widely used to prepare for olympiads and it is a useful tool to
<meta name="description" content="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?">
master and sharpen your skills and techniques in comptetitive problem solving. Some of these problems were a source
of inspiration for Jaan Kalda’s handouts and to some NBPhO problems. You may find problems from old IPhO
<meta property="og:title" content="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?">
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<meta property="og:description" content="A website with solutions to physics problems from Savchenko Textbook">
<meta property="og:description" content="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?">
<title>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?</title>
$1.1.21.$ 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?
$1.1.21.$ 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?
</p>
</p>
<center>
<center>
<figure>
<figure>
<img src="statement.png"
<img src="statement.png"
loading="lazy" width="230" />
loading="lazy" width="230" />
<figcaption>
<figcaption>
For problem $1.1.21$
For problem $1.1.21$
</figcaption>
</figcaption>
</figure>
</figure>
</center>
</center>
<p>
<p>
</p>
</p>
<h3>Solution</h3>
<h3>Solution</h3>
<p>
<p>
<p>
<p>
$a)$ Since the mirror in the $yOz$ plane reflects the beam along the $Ox$ axis, the $x$ coordinate is inverted.
$a)$ Since the mirror in the $yOz$ plane reflects the beam along the $Ox$ axis, the $x$ coordinate is inverted.
</p>
</p>
<p>
<p>
Thus, if $\vec{c_1}$ is the reflected ray from $\vec{c}$,
Thus, if $\vec{c_1}$ is the reflected ray from $\vec{c}$,
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$\vec{c_1} = (-c_x, c_y, c_z)$
$\vec{c_1} = (-c_x, c_y, c_z)$
</p>
</p>
<p>
<p>
$b)$ Similarly, the mirrors in the $yOx$ and $xOz$ planes reflect the beam along the $Oz$ and $Oy$ axes, respectively:
$b)$ Similarly, the mirrors in the $yOx$ and $xOz$ planes reflect the beam along the $Oz$ and $Oy$ axes, respectively:
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$\vec{c_2} = (c_x, c_y, -c_z)$, for$yOx$
$\vec{c_2} = (c_x, c_y, -c_z)$, for$yOx$
</p>
</p>
<p style="text-align: center;">
<p style="text-align: center;">
$\vec{c_3} = (c_x, -c_y, c_z)$, for $xOz$
$\vec{c_3} = (c_x, -c_y, c_z)$, for $xOz$
</p>
</p>
<p>
<p>
At reflection from three mirrors at once, all components of $\vec{c}$ will take their negative values:
At reflection from three mirrors at once, all components of $\vec{c}$ will take their negative values:
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
<small>All rights belong to the authors. <br> Commercial use of materials - with the written permission of the authors. <br> astrosander01@gmail.com <br></small>
