If the patient dose is 1 milligray (mGy) at a 72 inch source-to-image distance (SID), what will the patient dose be at a 40 inch SID?

To understand why the answer is 3.24 mGy, it is essential to apply the inverse square law, which states that the intensity of radiation is inversely proportional to the square of the distance from the source. In simpler terms, as you decrease the distance from the radiation source, the dose received increases significantly due to the radiation spreading out as it travels.

In this scenario, you have a patient dose of 1 mGy at a source-to-image distance (SID) of 72 inches. When you reduce the SID to 40 inches, the new dose can be calculated by taking the ratio of the distances.

Using the inverse square law formula:

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

Substituting the provided values gives:

[ \text{New Dose} = 1 \text{ mGy} \times \left( \frac{72}{40} \right)^2 ]

Calculating the ratio:

[ \left( \frac{72}{40} \right)^2 = \left( 1.8 \right)^2 = 3.