Question

A three-way bulb uses 50, 100, or 150 W of electrical power to deliver 665, 1620, or 2285 lm in its three settings. The bulb is placed 80 cm above a sheet of paper. If an illumination of at least 175 lx is needed on the paper, what is the minimum setting that should be used?

Answer 1

The minimum setting that should be used to achieve an illumination of at least 175 lx is the 100W setting.

Step-by-step explanation:

To determine the minimum setting that should be used to achieve an illumination of at least 175 lx on the paper, we need to find the power setting that can deliver the required luminous flux at the given distance. The illuminance on a surface can be calculated using the formula:

illuminance = luminous flux / (4 * π * distance^2)

Plugging in the values, we have:

For 50W setting: illuminance = 665 lm / (4 * π * 0.8^2) = 332 lx

For 100W setting: illuminance = 1620 lm / (4 * π * 0.8^2) = 810 lx

For 150W setting: illuminance = 2285 lm / (4 * π * 0.8^2) = 1140 lx

Therefore, the minimum setting that should be used to achieve an illumination of at least 175 lx is the 100W setting.