Using the inverse square law, what is the new exposure time if the target-to-film distance is doubled from 200mm to 400mm?

The inverse square law states that the intensity of radiation is inversely proportional to the square of the distance from the source of that radiation. In this context, it applies to how exposure time must change with changes in the target-to-film distance.

When the distance is increased from 200mm to 400mm, you are effectively doubling the distance. According to the inverse square law, if the distance is doubled, the intensity of radiation reaching the film is reduced to one-fourth of its original intensity (since ( (2)^2 = 4 )). This means that to maintain the same exposure level at the film, the exposure time must increase by a factor of four.

If the original exposure time at 200mm was 0.5 seconds, to achieve equivalent exposure at the new distance of 400mm, you would need to multiply the original time by 4:

0.5 seconds x 4 = 2.0 seconds.

Thus, the correct new exposure time at the increased distance of 400mm is 2.0 seconds, making this the accurate answer.