To establish the sequence of focal lengths for distinct colors in a convex lens, it is necessary to grasp the differential refraction of colors. Within a convex lens, the refractive index dictates the focal length for each color in the visible spectrum.
The refractive index is elevated for violet light and reduced for red light, correlated with violet light possessing a shorter wavelength and red light a longer wavelength.
The focal length \( f \) of a lens is inversely proportional to \( n-1 \), where \( n \) is the refractive index, expressed as \( f \propto \frac{1}{n-1} \). Consequently, a higher \( n \) results in a smaller \( f \).
The sequence of descending refractive indices, and thus ascending focal lengths, is as follows:
Therefore, the ascending order of focal lengths is: (A), (C), (D), (B).