A convex lens of focal length 40 cm forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length 20 cm. The photoelectric current now is :

Solution

Physics sir · 4 steps

The current counts photons per second, and the lens diameter decides that, not its focal length.

1. Light collected. A lens gathers light through its aperture. Both lenses have the same diameter, so each one collects the same light power from the source.
2. Image gets smaller. For a far-off extended source, the image size is proportional to f, so its area is proportional to f². Halving f from 40 cm to 20 cm makes the image area 1/4 as large.

   Intensity × Area = (4I₀) × A₀/4 = I₀ A₀ = same power

3. Photocurrent. The image is brighter, but the brightness gain exactly cancels the loss in area. The cell receives the same number of photons per second, and the photocurrent depends on that number.
4. So. The photoelectric current stays I, option (d).

The idea to keep. Photocurrent follows the total light power reaching the cell. Lens diameter sets how much light is gathered. Focal length only spreads it over a bigger or smaller image.

Answer from the NTA final answer key. Solution by PrepWiser.