Final answer:
The conversion factor related to brightness gain is approximately 2.67 times, based on a 37.5% conversion efficiency. This applies to light sources including stars, with brightness varying proportionally to the fourth power of mass. The Inverse Square Law for Light dictates how perceived brightness diminishes with distance, such as when observing distant stars like Alpha Centauri A.
Step-by-step explanation:
The conversion factor is approximately 2.67 times the brightness gain. This is derived from the inverse of the electrical conversion efficiency, which the EIA reports as being 37.5%. The concept is related to how power (like sunlight at roughly 1,000 W/m²) is converted into luminosity, which in turn relates to the brightness we perceive from a source, such as a light bulb or a star.
In astrophysics, luminosity can be approximated using the mass-to-luminosity relationship, where the brightness of a star varies as the fourth power of its mass - symbolized as L~M3.9. For example, if one star is twice the mass of another, it would be approximately 16 times brighter. Understanding this concept is essential when dealing with astronomical distances like with the star Alpha Centauri A, appearing significantly fainter due to its vast distance from Earth.
The Inverse Square Law for Light also plays a crucial role in how we perceive brightness. If the distance to a light source is doubled, the intensity of the light, or brightness, reduces to a quarter, following the inverse square principle. This law can be seen when determining the changes in intensity from a 120-W lightbulb at different distances, for instance.