Question

An image of the sun is formed by a lens, of the focal length of $30\,{\text{cm}}$, 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 $15\,{\text{cm}}$. The photoelectric current in this case is:
A. $\dfrac{I}{2}$
B. $I$
C. $2I$
D. $4I$

Answer 1

Recall the basics of the photoelectric cell and how photoelectric current is produced in the photoelectric cell. Check effect of change in focal length and diameter on the intensity of the light falling on the metal surface of the photoelectric cell. Also check the effect of change in diameter and focal length of the lens on the photoelectric current produced in the cell.

Complete answer:
We have been given that initially a lens of focal length $30\,{\text{cm}}$ is used to form the image of the sun. The light from the sun is collected by using this lens and incident on the metal surface of a photoelectric cell. The photoelectric current measured by the photoelectric cell corresponding to the light from the lens is $I$. For the second case, the lens used is replaced by the other lens of the same diameter but focal length $15\,{\text{cm}}$.We have asked to determine the photoelectric current measured by the photoelectric cell for the second case.

We know that the light gathered by the lens from the sun depends on the diameter of the lens and not on the focal length of the lens.Hence, even if the focal length of the lens is less than the initial lens, the diameter of the lens is the same. Hence, the amount of light collected by the lens is the same. This light is incident on the metal surface of the photoelectric cell and produces the same photoelectric current $I$.Therefore, the amount of the photoelectric current measured by the cell for the second case is $I$.

Hence, the correct option is B.

Note: The students may think that when the focal length of the lens is decreased then the area of the lens which is exposed to the radiations decreases which results in gathering of more light in a small area and intensity of the light falling on the metal surface increases resulting in more photoelectric current. But when the area decreases, the angle at which light is incident increases and the same photoelectric current is produced.