If a good cobalt-60 radiograph on a 3 inch steel casting requires 10 minutes at a source-to-film distance of 36 inches, what exposure time is needed at 24 inches?

To determine the exposure time needed at a different source-to-film distance, the principle of the inverse square law is applied. This law states that the intensity of radiation is inversely proportional to the square of the distance from the source. In practical terms, if you decrease the distance from the source, the intensity increases, requiring a shorter exposure time for the same level of film density.

In this case, the initial exposure time is 10 minutes at a source-to-film distance of 36 inches. When the distance is changed to 24 inches, the intensity of the radiation at this new distance will be greater because it is closer to the source.

First, we can calculate the ratio of the distances squared:

1. Calculate the square of the initial distance (36 inches): 36^2 = 1296.

2. Calculate the square of the new distance (24 inches): 24^2 = 576.

Next, we take the ratio of these two values:

[

\text{Ratio} = \frac{1296}{576} \approx 2.25

]

This means that at 24 inches, the intensity of radiation is about 2.25 times higher than at 36 inches. Since the exposure