Question #43212

A point source emitting both blue and red light is placed on the principal axis of a thin convex lens. The lens has a circular aperture of radius $R = 5 \text{ mm}$. The source is located at a distance $x_{1B} = 5 \text{ cm}$ from the first principal focus for blue light, and $x_{1R} = 3 \text{ cm}$ from the first principal focus for red light. The focal lengths of the lens are $f_B = 10 \text{ cm}$ and $f_R = 12 \text{ cm}$ for blue and red light, respectively.

The lens captures $N = 5 \times 10^{14}$ photons per second of each wavelength. A perfectly absorbing screen with a central circular aperture of radius $r_0 = 1 \text{ mm}$ is placed exactly at the image plane of the blue light. The light passing through this aperture strikes a large photoelectric detector.

Both wavelengths have sufficient energy to cause photoelectric emission. Assuming a quantum efficiency of $100\%$ (one photoelectron per incident photon) and ignoring diffraction effects, what is the saturation photoelectric current? (Use $e = 1.6 \times 10^{-19} \text{ C}$)