What new exposure time is required when changing from a 38-in. SID to a 42-in. SID while keeping other factors constant?

To determine the new exposure time when changing the Source-to-Image Distance (SID) from 38 inches to 42 inches while keeping other exposure factors constant, the inverse square law of radiation must be applied. This law states that the intensity of radiation decreases with the square of the distance from its source. Therefore, if the distance increases, the amount of radiation reaching the image receptor decreases, requiring a longer exposure time to maintain image receptor exposure.

The formula for the inverse square law is:

[ I_1 / I_2 = (D_2 / D_1)^2 ]

Where ( I_1 ) is the initial intensity, ( I_2 ) is the new intensity, ( D_1 ) is the initial distance (38 in.), and ( D_2 ) is the new distance (42 in.).

Calculating the exposure times involves knowing the original exposure time and adjusting it based on the ratio of the squares of the distances.

For the new exposure time:

1. Calculate the ratio of the distances:

(42 in / 38 in)² = (1.105)^2 ≈ 1.22

This means if the original exposure time was a certain value,