Question 17

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

Amount of light energy collected by a lens:

$$P \propto \text{Aperture Area} \propto D^2$$

Given: $$D_1 = D_2 = D \implies P_1 = P_2$$

Photoelectric current condition:

$$\text{Current } I \propto \text{Number of incident photons per second} \propto P$$

$$\text{Since } P \text{ remains unchanged} \implies I_{\text{new}} = I$$

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