When the distance of a point light source from a photocell is `r_(1)`, photoelectric current is `I_(1)`, If the distance becomes `r_(2)`, then the current is `I_(2)`, The ratio `(I_(1) : I_(2))` is equal to

Options

A. `r_(2)^(2) : r_(1)^(2)`
B. `r_(2) : r_(1)`
C. `r_(1)^(2) : r_(2)^(2)`
D. `r_(1) : r_(2)`

Explanation

To solve the problem, we need to find the ratio of photoelectric currents \( I_1 \) and \( I_2 \) when the distances from a point light source to a photocell change from \( r_1 \) to \( r_2 \).

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The photoelectric current \( I \) is proportional to the intensity of light \( I \). Therefore, we can write:
\[ I \propto \text{Intensity} \]

2. **Intensity of Light from a Point Source**:
The intensity \( I \) of light from a point source is given by the formula:
\[ I = \frac{P}{A} \]
where \( P \) is the power of the light source and \( A \) is the area over which the light is distributed.

3. **Calculating the Area**:
For a point source, the area \( A \) at a distance \( r \) is the surface area of a sphere:
\[ A = 4\pi r^2 \]
Therefore, the intensity at a distance \( r \) can be expressed as:
\[ I = \frac{P}{4\pi r^2} \]

4. **Finding Intensities at Distances \( r_1 \) and \( r_2 \)**:
- At distance \( r_1 \):
\[ I_1 = \frac{P}{4\pi r_1^2} \]
- At distance \( r_2 \):
\[ I_2 = \frac{P}{4\pi r_2^2} \]

5. **Calculating the Ratio of Intensities**:
To find the ratio \( \frac{I_1}{I_2} \):
\[ \frac{I_1}{I_2} = \frac{\frac{P}{4\pi r_1^2}}{\frac{P}{4\pi r_2^2}} = \frac{r_2^2}{r_1^2} \]

6. **Expressing the Ratio of Currents**:
Since \( I \propto \text{Intensity} \), we can say:
\[ \frac{I_1}{I_2} = \frac{r_2^2}{r_1^2} \]

7. **Final Ratio**:
Thus, the ratio of photoelectric currents \( I_1 : I_2 \) can be expressed as:
\[ I_1 : I_2 = r_2^2 : r_1^2 \]

### Conclusion:
The final answer is:
\[ (I_1 : I_2) = (r_2^2 : r_1^2) \]