If an x-ray exposure at 50 inches (127 cm) results in an intensity of 200 uGy, what would be the intensity at 40 inches (102 cm)?

To determine the intensity of x-rays at a different distance from the source, the inverse square law is applied. This law states that the intensity of radiation is inversely proportional to the square of the distance from the source. The formula is expressed as:

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

where ( I_1 ) and ( I_2 ) are the intensities at distances ( D_1 ) and ( D_2 ) respectively.

In this scenario, the initial intensity ( I_1 ) is 200 µGy at a distance ( D_1 ) of 50 inches. We need to find ( I_2 ) at a new distance ( D_2 ) of 40 inches. By substituting the values into the equation:

[ 200 , µGy / I_2 = (40^2) / (50^2) ]

Calculating the squares gives:

[ (40^2) = 1600 ]

[ (50^2) = 2500 ]

Now, plug these values into the equation:

[ 200 , µGy / I