Using the inverse square law, if the X-ray source moves from 90 cm to 30 cm away from the cassette, what will be the intensity change?

The inverse square law states that the intensity of radiation (in this case, X-rays) is inversely proportional to the square of the distance from the source. This law can be mathematically represented 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 distance changes from 90 cm (d1) to 30 cm (d2). Plugging these values into the formula:

[ I_{90} / I_{30} = (30^2 / 90^2) ] [ I_{90} / I_{30} = (900 / 8100) ] [ I_{90} / I_{30} = 1 / 9 ]

This shows that the intensity at 30 cm is 9 times greater than the intensity at 90 cm because:

[ I_{30} = 9 \times I_{90} ]

Therefore, when the source moves to a closer distance (from 90 cm to 30 cm