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Direct and Inverse Relationships The illuminance provided by a source
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of light has both a direct and an inverse relationship Math y
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If z is constant, then y is directly proportional to x When x increases, y increases When x decreases, y decreases If x is constant, then y is inversely proportional to z 2 When z 2 increases, y decreases When z 2 decreases, y increases
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If r is constant, then E is directly proportional to P When P increases, E increases When P decreases, E decreases If P is constant, then E is inversely proportional to r 2 When r 2 increases, E decreases When r 2 decreases, E increases
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Illumination of a Surface What is the illuminance at on your desktop if it is lighted by a 1750-lm lamp that is 250 m above your desk
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Assume that the lightbulb is the point source Diagram the position of the bulb and desktop Label P and r Known:
P r 175 103 lm 250 m
175 103 lm
250 m
Unknown:
Solve for the Unknown
The surface is perpendicular to the direction in which the light ray is traveling, so you can use the point source illuminance equation E
P 4 r2 175 103 m 4 (250 m)2
Substitue P
175 103 lm, r
250 m
Math Handbook
Operations with Significant Digits pages 835 836
223 223 lx
lm/m2
Evaluate the Answer
Are the units correct The units of luminance are lm/m2 lx, which the answer agrees with Do the signs make sense All quantities are positive, as they should be Is the magnitude realistic The illuminance is less than the luminous flux, which it should be at this distance
1 A lamp is moved from 30 cm to 90 cm above the pages of a book Compare the illumination on the book before and after the lamp is moved 2 What is the illumination on a surface that is 30 m below a 150-W incandescent lamp that emits a luminous flux of 2275 lm 3 Draw a graph of the illuminance produced by a 150-W incandescent lamp between 050 m and 50 m 4 A 64-cd point source of light is 30 m above the surface of a desk What is the illumination on the desk s surface in lux 5 A public school law requires a minimum illuminance of 160 lx at the surface of each student s desk An architect s specifications call for classroom lights to be located 20 m above the desks What is the minimum luminous flux that the lights must produce 6 A screen is placed between two lamps so that they illuminate the screen equally, as shown in Figure 16-7 The first lamp emits a luminous flux of 1445 lm and is 25 m from the screen What is the distance of the second lamp from the screen if the luminous flux is 2375 lm
P 2375 lm
Screen
25 m P 1445 lm
Figure 16-7 (Not to scale)
16 Fundamentals of Light
Engineers who design lighting systems must understand how the light will be used If an even illumination is needed to prevent dark areas, the common practice is to evenly space normal lights over the area to be illuminated, as was most likely done with the lights in your classroom Because such light sources do not produce truly even light, however, engineers also design special light sources that control the spread of the light, such that they produce even illuminations over large surface areas Much work has been done in this field with automobile headlights
The Speed of Light
For light to travel from a source to an object to be illuminated, it must travel across some distance According to classical mechanics, if you can measure the distance and the time it takes to travel that distance, you can calculate a speed Before the seventeenth century, most people believed that light traveled instantaneously Galileo was the first to hypothesize that light has a finite speed, and to suggest a method of measuring its speed using distance and time His method, however, was not precise enough, and he was forced to conclude that the speed of light is too fast to be measured over a distance of a few kilometers Danish astronomer Ole Roemer was the first to determine that light does travel with a measurable speed Between 1668 and 1674, Roemer made 70 measurements of the 18-day orbital period of Io, one of Jupiter s moons He recorded the times when Io emerged from Jupiter s shadow, as shown in Figure 16-8 He made his measurements as part of a project to improve maps by calculating the longitude of locations on Earth This is an early example of the needs of technology driving scientific advances After making many measurements, Roemer was able to predict when the next eclipse of Io would occur He compared his predictions with the actual measured times and found that Io s orbital period increased on average by about 13 s per orbit when Earth was moving away from Jupiter and decreased on average by about 13 s per orbit when Earth was approaching Jupiter Roemer believed that Jupiter s moons were just as regular in their orbits as Earth s moon; thus, he wondered what might cause this discrepancy in the measurement of Io s orbital period
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