Question

The​ intensity, I, of light received at a source varies inversely as the square of the​ distance, d, from the source. If the light intensity is 83 ​foot-candles at ​35 feet, find the light intensity at 7 feet.

Answer 1

The light intensity at 7 feet is approximately 1407 foot-candles.

Step-by-step explanation:

The intensity of light received at a source varies inversely as the square of the distance from the source. This means that as the distance from the source decreases, the intensity of light increases. To find the light intensity at 7 feet, we can use the inverse square law formula.

Given:
Intensity (I) = 83 foot-candles
Distance (d) = 35 feet

The formula for the inverse square law is:

I1 * d1^2 = I2 * d2^2

Substituting the given values:

83 * 35^2 = I2 * 7^2

Simplifying this equation, we can solve for I2, which represents the light intensity at 7 feet.

I2 = (83 * 35^2) / (7^2)

Calculating this, we find that the light intensity at 7 feet is approximately 1407 foot-candles.