Final answer:
The individual chromosomes become visible during the prophase stage of mitosis, which is the initial phase involving chromosome condensation. Prophase is also marked by the disappearance of the nucleolus and disintegration of the nuclear envelope.
Step-by-step explanation:
The Visible Chromosomes in Mitosis
The individual chromosomes become visible with a light microscope during the prophase stage of mitosis. Prophase is the initial phase where the loosely packed chromatin coils up and condenses into more distinctly observable structures. Each chromosome then becomes visible as an X-shaped entity consisting of two identical sister chromatids. The nucleolus fades and the nuclear envelope breaks apart during this stage, setting the stage for subsequent mitotic processes.
As for the attachment of the mitotic spindle fibers to the kinetochores, which is a characteristic event for ensuring proper chromosome segregation, it occurs typically during prometaphase, following prophase and just before metaphase.