Question

A lumen is a unit of measurement of the total quantity of visible light. Suppose the intensity of light from a light source varies inversely with the distance from the light source. The intensity of the light 100 inches from a light source is 60 lumens. Determine the intensity of the same light 150 inches from its source.

Answer 1

The intensity of light \( I \) varies inversely with the distance \( d \) from the light source, which can be expressed mathematically as:

\[ I = \frac{k}{d} \]

where \( k \) is a constant.

Given that the intensity at a distance of 100 inches is 60 lumens, we can first calculate the constant \( k \):

\[ 60 = \frac{k}{100} \]

Multiplying both sides by 100 gives:

\[ k = 60 \times 100 = 6000 \]

Now that we have the constant \( k \), we can determine the intensity at a distance of 150 inches.

Using the inverse variation formula:

\[ I = \frac{6000}{150} \]

Performing the division:

\[ I = 40 \]

Thus, the intensity of the light at a distance of 150 inches from the source is \( \boxed{40} \) lumens.