Solve problems involving the proportional relationship between intensity of light and the inverse-square of the distance from the source using 𝐼 ∝ 1 𝑟2.

A lamp is placed at a distance of 2.0 m from a light sensor, producing an intensity reading of 120 W m⁻². Describe the relationship between intensity and distance for this light source, and state the intensity if the sensor is moved to 4.0 m from the lamp.

A point light source is positioned at a fixed location. The intensity of light is measured at two different distances from the source, \(r_1 = 2.0\) m and \(r_2 = 6.0\) m. The intensity at \(r_1\) is \(I_1 = 45\) W m\(^{-2}\). What is the intensity \(I_2\) at distance \(r_2\)?

A student measures the light intensity from a point source at three different distances and records the data in the table below. Determine whether the student's data supports the inverse-square law relationship for light intensity. Justify your conclusion using specific values from the data.

Two identical light sources, A and B, are placed at different distances from a detector. Source A is 2.0 m from the detector and produces an intensity of 64 W/m² at the detector. Source B produces an intensity of 16 W/m² at the same detector. Compare the distance of source B from the detector to that of source A, and justify your answer using the inverse-square relationship.