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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.