If the patient dose is 1 milligray (mGy) at a 40-inch (102 cm) SID, what would be the dose at a 72-inch (183 cm) SID?

To determine how the patient dose changes with a change in Source-to-Image Distance (SID), 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.

Given that the initial dose is 1 mGy at a distance of 40 inches (102 cm), we can calculate the dose at a new distance of 72 inches (183 cm). The relationship can be mathematically defined as follows:

[ \text{New Dose} = \text{Old Dose} \times \left( \frac{\text{Old SID}}{\text{New SID}} \right)^2 ]

By substituting the values into the equation:

1. Old Dose = 1 mGy

2. Old SID = 40 inches

3. New SID = 72 inches

The calculation of the ratio of the SIDs is:

[ \frac{40}{72} = \frac{5}{9} ]

Then we square this ratio:

[ \left( \frac{5}{9} \right)^2 = \frac{25}{81} ]

Now we can find the new dose:

[ \text{New Dose} = 1