Applications - A Guide to MATLAB for Beginners and Experienced Users - page 144

d = 0:0.1:5;
for x = 0:0.5:5
plot(d, light3(x, 0, d) + light3(x, 0, 5) + ...
light3(x, 0, 10 - d))
hold on

end
hold off

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 know that for d near 5, the intensity will be increasing as x increases
from 0 to 5, so the bottom curve corresponds to x = 0 and the top curve to
x = 5. Notice that the x = 0 curve is the lowest one for all d , and it rises as d
decreases. Thus d = 0 maximizes the intensity of the darkest spots in the
room, which are the corners (corresponding to x = 0). There the intensity is
as follows:

light3(0, 0, 0) + light3(0, 0, 5) + light3(0, 0, 10)

ans =
0.8920

This is surprising; we do worse than with two bulbs. In going from two
bulbs to three, with a decrease in wattage per bulb, we are forced to move
wattage away from the ends of the room and bring it back to the center. We
could probably improve on the two-bulb scenario if we used brighter bulbs at
the ends of the room and a dimmer bulb in the center, or if we used four
75-watt bulbs. But our results so far indicate that the amount to be gained in
going to more than two bulbs is likely to be small compared with the amount
we gained by going from one bulb to two.