The brightness of a light bulb varies inversely as the square of the distance from the source. If a light bulb has a brightness of 300 lumens at 2 ft, what will its brightness be at 10 ft?
To find the brightness at 10 ft, we can use the formula for inverse variation:
brightness = k/distance^2
where k is the constant of variation.
Given that the brightness is 300 lumens at 2 ft, we can substitute these values into the formula:
300 = k/2^2
To find the value of k, we can solve for it:
k = 300 * 2^2
k = 1200
Now we can substitute k into the formula and find the brightness at 10 ft:
brightness = 1200/10^2
brightness = 1200/100
brightness = 12 lumens
Therefore, the brightness of the light bulb at 10 ft will be 12 lumens.
To solve this problem, we need to use the inverse square law for light intensity, which states that the brightness of a light source is inversely proportional to the square of the distance from the source.
Let's break down the problem and find the formula that relates the brightness and distance.
Given:
Brightness = 300 lumens
Distance from the source = 2 ft
Let's represent the brightness as B and the distance as d. According to the inverse square law, we have:
B ∝ 1/d²
We can write this as:
B = k/d²
where k is a constant of proportionality. To find the value of k, we can substitute the given values:
300 = k/(2²)
300 = k/4
k = 1200
Now that we have the value of k, we can use it to find the brightness at a different distance. Let's find the brightness at 10 ft.
B = 1200/(10²)
B = 1200/100
B = 12 lumens
Therefore, the brightness of the light bulb at 10 ft will be 12 lumens.