Greenwood press

REFLECTIONS
107
Boats and buildings reflected
in a canal in Holland.
Source: Adobe Stock Photos.
A kaleidoscope uses mirrors to produce mul-
tiple reflections and create colorful patterns.
Photo by Dror Bar-Natan, online at
www.ma.huji.ac.il/~drorbn/Gallery/Symmetry
/Tilings/S333/Kaleidoscope.html>.

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Reflections can be used to trap light in an object. When a gem such as a dia-
mond is cut into the shape of a polyhedron, it gives light an opportunity to reflect
many times once it is captured inside. One of the reasons that a diamond is pre-
cious is its ability to bend light so that it stays inside the gem longer, thus mak-
ing it sparkle. 
Sound waves reflect in a theater to amplify music. Prior to electronic ampli-
fiers, which increase the volume of microphones and electric guitars at rock con-
certs, special attention was paid to acoustical architecture in concert halls. Next
time you watch a performance or a symphony in an indoor theater, notice the spe-
cial plates built in or attached to the ceiling. They are angled and curved in order
to reflect sound waves so that everyone in the theater can hear the performance.
Without this special attention to reflecting sound waves, certain sections of the
concert hall would not receive adequate sound, because the sound would either
be absorbed by a surface, dissipate, or create destructive interference patterns.
(See Inverse Square Function.)
Reflections are also used in remote sensors to detect a signal. For example,
there are several ways that you can change your television station using a remote
control. One way is to aim the remote so that its ray will land directly on the sen-
sor on the television set. Another way, however, is to aim the remote at a reflec-
tion of the sensor. Imagine that one of the walls in your home was a reflecting
mirror, and determine the location of the television sensor behind the wall. If you
aim the remote at the reflection of the sensor, the light beam will bounce off of
the wall and land directly on the sensor. Many motion-based security systems
operate in a similar fashion. An invisible beam reflects off of all walls in a room,
creating multiple beams throughout that room. The alarm system is signaled if
the beam at any point in the room is disturbed.
The angle of incidence, 
α, is the angle at which a beam of light touches a wall,
and the angle of reflection, 
β, is the angle at which the beam leaves the wall. If
the beam of light does not pass through the material, then the angle of incidence
is equal to the angle of reflection. (See Angle for more explanation.) Knowing this
theorem can help you become skilled at various games that use reflections, such
as billiards and miniature golf. In both of these activities, the player is usually at
an advantage if he or she can find ways to maneuver the ball by bouncing it off of
a wall. In order to accurately place a ball on a target or in a hole, the player needs
to aim the ball towards the reflection of the hole, similar to directing a remote con-
trol. Therefore an easier way to utilize the reflection is to predict the location on
the wall where the angle of incidence will equal the angle of reflection.