How do you calculate the total power of a lens with both spherical and cylindrical components?

To calculate the total power of a lens that includes both spherical and cylindrical components, vector addition is employed because these components affect light in different ways. The spherical component contributes to focusing light in all directions, while the cylindrical component only focuses light in one specific direction.

When combining these two types of power, it's essential to consider their vector nature, whereby the spherical power can be thought of as acting uniformly across all meridians, and the cylindrical power acts as a vector that modifies the sphere's power in a particular axis.

This approach allows for an accurate representation of how the lens will function when it is being used, leading to a more precise total power that can be distinctly measured. In practical terms, this means breaking down the components into their vector forms, which can then be combined to yield the overall effective power of the lens system.