Question

The photoelectric currents at distances $r_1$ and $r_2$ of light source from photoelectric cell are $I_1$ and $I_2$ respectively. The value of $I_1/$$I_2$ will be

• A. $\frac{r_1}{r_2}$
• B. $\frac{r_2}{r_1}$
• C. ${\left(\frac{r_1}{r_2}\right)}^2$
• D. ${\left(\frac{r_2}{r_1}\right)}^2$

Answer 1

The correct option is D ${\left(\frac{r_2}{r_1}\right)}^2$

The intensity of incident light is given by

$i=\frac{P}{4\pi r^2}$

where, variables have their usual meanings.
The photocurrent is directly proportional to the intensity of incident light.
Therefore photocurrent is inversely proportional to the square of distance of light source from photoelectric cell.

hence, $I_1\propto \frac{1}{r_1^2}$ and $I_2\propto \frac{1}{r_2^2}$

$\Rightarrow \frac{I_1}{I_2}=\frac{r_2^2}{r_1^2}$

$\Rightarrow \frac{I_1}{I_2}=(\frac{r_2}{r_1}{)}^2$

So, the answer is option (D).