The intensity of light varies inversely with the distance from the light source. This can be expressed mathematically with the formula:
\[ I = \frac{k}{d} \]
where \( I \) is the intensity, \( d \) is the distance from the source, and \( k \) is a constant of proportionality.
Given that the intensity of light at 100 inches is 60 lumens:
\[ I_1 = 60 \text{ lumens} \] \[ d_1 = 100 \text{ inches} \]
We can find the constant \( k \):
\[ 60 = \frac{k}{100} \]
Multiplying both sides by 100 gives:
\[ k = 60 \times 100 = 6000 \]
Now, we need to find the intensity \( I_2 \) at a distance \( d_2 = 150 \) inches. Using the same formula:
\[ I_2 = \frac{k}{d_2} = \frac{6000}{150} \]
Now, calculate:
\[ I_2 = \frac{6000}{150} = 40 \text{ lumens} \]
Thus, the intensity of the light 150 inches from the source is 40 lumens.
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