If a follow spot puts out 100fc at 200 ft with a 40ft beam size, what is the beam size and foot candles at 100 ft?

To determine the beam size and foot candles at a distance of 100 feet, it's essential to understand the concepts of beam spread and the inverse square law, which states that light falls off in intensity relative to the square of the distance from the source.

At 200 feet, the follow spot provides 100 foot candles (fc) at a beam size of 40 feet. To find out how this changes at 100 feet, we first evaluate how the intensity is affected by the distance reduction:

1. The distance from 200 feet to 100 feet is halved, so the intensity of the light will increase by a factor of four since the distance is squared when applying the inverse square law. Therefore, the illumination at 100 feet can be calculated as follows:

[

\text{Foot candles at 100 ft} = 100 , \text{fc} \times (200 , \text{ft}/100 , \text{ft})^2 = 100 , \text{fc} \times 4 = 400 , \text{fc}

]

2. The beam size also changes based on the distance. Since the overall dimensions of the light remain proportional, and