Graphics Programs Reference
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either at the corners or at the midpoints of the two long walls. By symmetry,
the intensity will be the same at all four corners, so let's graph the intensity
at one of the corners (0, 0) as a function of
d
.
d = 0:0.1:5; plot(d, light2(0, 0, d) + light2(0, 0, 10 - d))
1.05
1
0.95
0.9
0.85
0.8
0.75
0.7
0.65
0.6
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
As expected, the smaller
d
is, the brighter the corners are. In contrast, the
graph for the intensity at the midpoint (5, 0) of a long wall (again by
symmetry it does not matter which of the two long walls we choose) should
grow as
d
increases toward 5.
plot(d, light2(5, 0, d) + light2(5, 0, 10 - d))
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
We are after the value of
d
for which the lower of the two numbers on the
above graphs (corresponding to the darkest spot in the room) is as high as
possible. We can find this value by showing both curves on one graph.
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