Final answer:
To find the light intensity at 7 meters using the inverse square law, one must establish the constant of proportionality with given values, then use that constant to calculate the new intensity.
Step-by-step explanation:
The student's question falls under the topic of the inverse square law for light intensity, which is a principle in physics that applies to various types of physical quantities. According to this law, the intensity (I) of light from a source (like a bulb) varies inversely with the square of the distance (D) from the source. In mathematical terms, this relationship is expressed as I ∝ 1/D².
Given that the intensity of light is 108 lumens at a distance of 12 meters, and we want to find the intensity at a 7-meter distance, we first establish the constant of proportionality (k) using the initial conditions. So we have I1 ∝ 1/D1² and I1 = 108 lumens, D1 = 12 meters, resulting in k = I1 × D1² = 108 lumens × (12 m)².
Now, to find the new intensity (I2) at D2 = 7 meters, we rearrange the formula to solve for I2: I2 = k / D2². Plugging in the known values, we get I2 = k / (7 m)². By computing this, we determine the new intensity at 7 meters.