Final answer:
To maintain the same image density when changing from a 200-speed to an 800-speed screen-film system, the new milliampere-seconds value required would be 10 mAs. This is calculated by dividing the original mAs by 4, because the new screen is 4 times faster.
Step-by-step explanation:
The question is asking what new milliampere-seconds (mAs) value would be required to produce the same density if the screen-film system speed changes from 200 speed to 800 speed for radiographic imaging. The relationship between the screen speed and the required mAs to maintain density is that if the screen speed is increased, the necessary mAs can be decreased, because a faster screen requires less exposure to produce the same image density.
Since the speed of the screen-film system increases by a factor of 4 (from 200 to 800), you would need to reduce the exposure by the same factor to maintain image density. Therefore, you would divide the original mAs value by 4.
The calculation would be:
Original mAs: 40 mAs
New screen speed: 800 (4 times the original speed of 200)
New mAs value: 40 mAs / 4 = 10 mAs