Final answer:
Increasing the SID from 40 to 48 inches requires an increase in the mAs to maintain image exposure due to the inverse square law. It would neither decrease the mAs by half nor by 25%; the mAs must be increased. Additionally, an increase in SID would decrease the penumbra in the radiographic image.
Step-by-step explanation:
The question involves understanding the relationship between the Source-to-Image Distance (SID) and the milliampere-seconds (mAs) in radiographic imaging, a concept within the realm of physics, more specifically involving principles of radiology and optics. Increasing the SID from 40 inches to 48 inches increases the distance between the X-ray source and the image receptor. According to the inverse square law, the intensity of the X-ray beam at the image receptor will decrease as the square of the distance from the source increases, which means that when the distance increases, the mAs should be adjusted to maintain the same exposure. The inverse square law can be mathematically expressed as:
I1 d2^2
------ = -----
I2 d1^2
where I1 and I2 are the beam intensities and d1 and d2 are the distances at two different SIDs. If the SID increases from 40 to 48 inches, we get:
I1 (48)^2
------ = -----
I2 (40)^2
This simplifies to:
I1 48^2
------ = -----
I2 40^2
I1 2304
------ = -----
I2 1600
The intensity at the original SID (I2) will be stronger than at the increased SID (I1). So, we need to adjust the mAs to compensate for this difference. To find the new mAs value (mAs1), we can set up a proportion with the original mAs value (mAs2):
mAs1 I2
------- = ----
mAs2 I1
Since I1 is less than I2 because of the increased distance, it is clear that mAs1 will need to be increased to maintain the same exposure. Without actual mAs values, we can't calculate the precise new value, but we do know that the mAs will not decrease by half or by 25%; conversely, it must be increased to account for the decreased intensity due to the increased distance. Furthermore, penumbra, or edge blurriness of an image, would actually decrease with an increased SID because a greater distance lessens the geometric unsharpness.