Question

the brightness or intensity, i, of light observed at a distance, d, from the source of the light is given by the formula i = \frac{k}{d^{2}}, where k is positive constant. which is the effect on the intensity of the light if the distance from the light source is doubled? a. the intensity will be four times as great. b. the intensity will be two times as great. c. the intensity will be one - half as great. d. the intensity will be one - fourth as great.

Explanation:

Step1: Define initial situation

Let the initial distance be $d_1 = d$, then the initial intensity $I_1=\frac{k}{d^{2}}$.

Step2: Define new situation

The new distance $d_2 = 2d$. Substitute $d_2$ into the formula: $I_2=\frac{k}{(2d)^{2}}$.

Step3: Simplify new - intensity formula

$I_2=\frac{k}{4d^{2}}$.

Step4: Compare $I_1$ and $I_2$

Since $I_1=\frac{k}{d^{2}}$ and $I_2=\frac{k}{4d^{2}}$, we can see that $I_2=\frac{1}{4}I_1$. So when the distance is doubled, the intensity is one - fourth as great.

Answer:

D. The intensity will be one - fourth as great.