An image of the sun is formed by a lens, of the focal length of 30 cm, on the metal surface of a photoelectric cell and a photoelectric current I is produced. The lens forming the image is then replaced by another of the same diameter but of focal length 15 cm. The photoelectric current in this case is

Options

A. `(I)/(2)`
B. I
C. 2I
D. 4I

Explanation

To solve the problem, we need to analyze the effect of changing the focal length of the lens on the photoelectric current produced in the photoelectric cell.

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have a photoelectric cell where sunlight is focused using a lens.
- The first lens has a focal length of 30 cm, and it produces a photoelectric current \( I \).

2. **Replacing the Lens**:
- The first lens is replaced by another lens with the same diameter but a shorter focal length of 15 cm.

3. **Intensity and Photoelectric Current**:
- The intensity of light (which is related to the number of photons hitting the surface per unit area per second) is what determines the photoelectric current.
- The photoelectric current \( I \) is directly proportional to the intensity of light incident on the photoelectric cell.

4. **Relation Between Focal Length and Intensity**:
- The intensity of light at the photoelectric cell depends on how much light is focused onto the area of the cell.
- The intensity of light is also related to the area over which the light is spread. A lens with a shorter focal length focuses light more tightly, but this does not affect the total number of photons (or the intensity) that are produced by the sun.

5. **Conclusion**:
- Since the intensity of light and thus the number of photons hitting the photoelectric cell does not depend on the focal length of the lens, the photoelectric current produced remains the same.
- Therefore, the photoelectric current with the second lens is also \( I \).

### Final Answer:
The photoelectric current in the second case is \( I \).

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