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.