The illumination produced by a light source is inversely proportional to the square of the distance to the source. If a light source 5m from an object illuminates with 70 candela, what illumination would be produce if the object were mover to 12 m away?
not sure how to set this up
To solve this problem, we can use the inverse square law for illumination. The inverse square law states that the illumination produced by a light source, in this case measured in candela (cd), is inversely proportional to the square of the distance from the source.
Let's set up the equation using this information:
I₁ = Illumination at distance 1 (5m)
I₂ = Illumination at distance 2 (12m)
d₁ = Distance 1 (5m)
d₂ = Distance 2 (12m)
According to the inverse square law:
I₁ = k / d₁²
I₂ = k / d₂²
where k is a constant.
We know that I₁ is 70 candela at distance 1 (5m). Using this information, we can find the value of k:
I₁ = k / d₁²
70 = k / 5²
70 = k / 25
To find the value of k, we can cross multiply:
k = 70 * 25
k = 1750
Now that we have the value of k, we can use it to find the illumination at distance 2 (12m):
I₂ = k / d₂²
I₂ = 1750 / 12²
I₂ = 1750 / 144
Calculating this gives us:
I₂ ≈ 12.15 candela
Therefore, if the object is moved to 12m away from the light source, the estimated illumination produced would be approximately 12.15 candela.