Final answer:
The formula to adjust IR signal intensity when the distance changes is 'Intensity 1/Intensity 2 = D2 squared/D1 squared', which is derived from the inverse square law stating that the intensity of light or IR is inversely proportional to the square of its distance from the source.
Step-by-step explanation:
The correct formula to adjust for a change in distance to maintain signal intensity for infrared (IR) and other forms of light is D. Intensity 1/Intensity 2 = D2 squared/D1 squared. This equation stems from the inverse square law for light, which states that the intensity of light (or in this case, the IR signal) is inversely proportional to the square of the distance from the source.
If, for example, the distance from an IR emitter is doubled, the intensity of the signal at the new distance would be one fourth of the original intensity because the square of 2 (the factor by which the distance was increased) is 4.
To apply this concept in practice, if the original intensity of an IR source was measured at 2.4 W/m² at a distance of 2 m, doubling the distance to 4 m would result in a new intensity of 0.6 W/m², given that (2 m) squared is 4 and (4 m) squared is 16, and thus 4 W/m² divided by 16 equals 0.6 W/m². This demonstrates how the intensity decreases with the inverse square of the distance.