Final answer:
In this case, the bulb must be placed approximately 2.165 cm away to produce a light intensity of 750 lux.
Step-by-step explanation:
To determine the distance at which the bulb must be placed to produce a light intensity of 750 lux, we can use the inverse square law for light intensity.
Here's how we can calculate it step-by-step:
1. We know that the bulb gives out a light intensity of 4000 lux at a distance of 5 cm.
2. The inverse square law states that the intensity of light is inversely proportional to the square of the distance from the source. In other words, as the distance increases, the intensity decreases.
3. We can set up a proportion to find the distance at which the light intensity is 750 lux.
Let's say x represents the distance in centimeters:
4000 lux / (5 cm)² = 750 lux / (x cm)²
4. Now, we can solve for x by cross-multiplying:
4000 lux * (x cm)² = 750 lux * (5 cm)²
5. Simplifying further:
(x cm)² = (750 lux * (5 cm)²) / 4000 lux
6. Continuing the calculation:
(x cm)² = (750 lux * 25 cm²) / 4000 lux
(x cm)² = 18750 cm² / 4000 lux
(x cm)² = 4.6875 cm²
7. Taking the square root of both sides to solve for x:
x cm = √4.6875 cm²
8. Simplifying:
x cm ≈ 2.165 cm
Therefore, the bulb must be placed approximately 2.165 cm away to produce a light intensity of 750 lux.