Theory of Vergences

• Introduction
• Vergences
• Mirrors
• Interfaces
• Magnification
• Thin Lenses
• Combinations
• Aberrations
• Summary
• Examples

Summary

The main equations and sections are summarised below.

1. Vergences:

V_i = ±n/u, V_f = ±n/v, + converging, - diverging

2. Powers:

Mirror: P = ±2n/r

Interface: P = ±|n₂-n₁|/r

Lens in air: P = 1/f where f is the focal length

+ causes convergence, - causes divergence

Units are Dioptres D(m^-1)

3. Vergence Equation (for all optics):

V_f = P + V_i

4. Magnification (for all optics):

m = V_i/V_f

+ upright

- inverted

5. Complex optics:

Surfaces in contact => can add Powers

Otherwise must treat each surface separately

6. Aberrations:

Spherical - off axis rays don't focus to same point

Chromatic - focal point location is wavelength dependent