Given a beam intensity of 90 μGy at 38 inches, what is the intensity at 48 inches?

To solve the problem of determining the intensity of a beam at a different distance, we can apply the inverse square law, which states that the intensity of radiation (or light) from a point source is inversely proportional to the square of the distance from the source. This means that as the distance from the source increases, the intensity decreases according to the formula:

[ I_1 \times d_1^2 = I_2 \times d_2^2 ]

In this particular scenario, we know the initial intensity (90 μGy) and the distances (38 inches and 48 inches). We need to find the intensity at 48 inches (I_2).

By rearranging the formula, we get:

[ I_2 = I_1 \times \left( \frac{d_1}{d_2} \right)^2 ]

Plugging in the values:

• ( I_1 = 90 , \mu Gy )

• ( d_1 = 38 , \text{inches} )

• ( d_2 = 48 , \text{inches} )

Calculating this, we have:

[ \left( \frac{38}{48