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How can we use
this formula to make a parabolic mirror?
To convert this into
actual dimensions used to make the wooden frame to carry the mirror we
can draw up a table. (We will turn the equation around in terms of x rather
than y i.e. x = y2 / 4a so by putting in various values of
y we can get corresponding values for x). Y is the distance along from
the center of the mirror and x is the height above the lowest part of
the mirror.
For a mirror with
a focus point one-half meter (19.7 in.) above the bottom of the mirror we get the
following table:
y (meters) |
y2
|
y2
/ (4 x a) |
height of
mirror |
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0 |
0.01
0.04
0.09
0.16
0.25
0.36
0.47
0.64
0.81
1.00 |
0.005
0.020
0.045
0.080
0.125
0.185
0.235
0.320
0.405
0.500 |
5mm
2cm
4.5cm
8cm
12.5cm
18.5cm
23.5cm
32cm
40.5cm
50cm |
Using these figures
we can make a wooden frame made up of vertical wooden supports fixed to
a flat board. The height of each vertical support is given in the right
hand column of the table for various distances out from the center (y).
A thin wooden sheet was then placed on top to form the parabola on which
to fix the mirror.
Attaching the mirror 
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