Determine The Intensity Of The Lamp, Illuminance At Point

Determine the intensity of the lamp, the illuminance at point B, and the effect of mounting a

Analyze a roof-mounted lamp used for general lighting in a room, given the illuminance directly below it at point A as 200 lux. Assume the lamp radiates uniformly in all downward directions. Determine the intensity of the lamp based on the provided data. Next, calculate the illuminance at point B, which is located in the room, considering the lamp's properties and location. Finally, if a new lamp with an intensity of 900 cd is mounted directly above point B, evaluate the combined illumination at point B when both lamps are operating.

Paper For Above instruction

Lighting design is a crucial aspect of interior and architectural projects, dictating not only the aesthetic appeal but also the safety and functionality of spaces. When designing lighting systems, understanding the fundamental parameters such as luminous intensity, illuminance, and the effects of multiple lamps is essential. In this paper, we analyze a typical lighting scenario involving a roof-mounted lamp, aiming to determine its luminous intensity, the resulting illuminance at a specified point, and the impact of introducing an additional light source.

Analysis of the Lamp's Intensity

The problem provides that the illuminance directly beneath the lamp at point A is 200 lux. Assuming the lamp emits light uniformly in all directions, the relationship between luminous intensity (I) and illuminance (E) is expressed by the inverse square law:

E = I / R^2,

where R is the distance from the lamp to the point where illuminance is measured.

Rearranged to find the luminous intensity, I = E × R^2. However, the distance R from the lamp to point A is not explicitly specified in the problem. Presuming the measurement at point A is taken at a known distance, R, from the lamp, the calculation proceeds accordingly. If R is, for example, 3 meters, then

I = 200 lux × (3 m)^2 = 200 × 9 = 1800 cd.

Thus, the luminous intensity of the lamp is estimated at 1800 candela based on the assumed distance.

Calculating Illuminance at Point B

Next, to determine the illuminance at point B, located at a different position in the room, we consider the inverse square law again, factoring in the distance from the lamp to point B. If the distance from the lamp to point B is R_b, the illuminance E_b at point B can be calculated as

E_b = I / R_b^2.

Assuming that R_b is known or can be measured—for instance, R_b might be 4 meters—the illuminance at point B becomes

E_b = 1800 cd / (4)^2 = 1800 / 16 = 112.5 lux.

This value illustrates how illuminance diminishes with increasing distance from the light source, following the inverse square law.

Effect of Mounting a New Lamp Above Point B

Now, consider the addition of a second lamp directly above point B, with a luminous intensity of 900 cd. The total illuminance at point B is the sum of the contributions from both lamps, assuming no interference and that light combines additively in the space.

For the second lamp, if it is located right above point B at a negligible distance, its contribution simplifies to the luminous intensity divided by the area of the sphere if considering the luminous intensity directly. Alternatively, if the second lamp is also at a known distance R_b, then its contribution is

E_{second} = 900 / R_b^2.

Using the same R_b of 4 meters, the illuminance from the second lamp at point B would be

E_{second} = 900 / 16 = 56.25 lux.

Adding this to the initial 112.5 lux yields a total illuminance of approximately 168.75 lux at point B when both lamps are turned on.

Conclusion

This analysis demonstrates the importance of understanding luminous intensity and the inverse square law's role in lighting calculations. The initial lamp’s intensity was deduced from measured illuminance, and the effect of an additional light source was assessed by simple additive principles. These calculations aid in designing adequate lighting systems that meet illumination standards and ensure visual comfort in indoor environments.

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