Given a radiograph using a 36-in. SID and 12 mAs, what should the new milliampere-seconds value be at a 42-in. distance using a 5:1 grid?

To determine the new milliampere-seconds (mAs) value when changing the source-to-image distance (SID) from 36 inches to 42 inches, it's essential to understand how distance affects the exposure in radiographic imaging.

When the SID increases, the intensity of the radiation reaching the film or detector decreases due to the inverse square law, which states that radiation exposure decreases with the square of the distance from the source. To maintain the same exposure on the film, the mAs must be adjusted accordingly.

The adjustment can be calculated using the formula:

New mAs = Old mAs × (New SID / Old SID)²

Given the original mAs of 12 mAs and the old SID of 36 inches, we can substitute the values as follows:

1. New SID = 42 inches

2. Old SID = 36 inches

3. Old mAs = 12 mAs

Now, applying the formula:

New mAs = 12 mAs × (42 / 36)²

New mAs = 12 mAs × (1.1667)²

New mAs = 12 mAs × 1.3611 ≈ 16.33 mAs

However,