Geometric and Physical Optics
Vergence and power
Vergence is L = n / l, with l in meters; light diverging from a point 0.5 m away in air carries −2.00 D of vergence. A thin lens of focal length f (meters) has power F = 1/f. Surface power is F = (n₂ − n₁) / r. Vergences combine only after converting for reduced distance across separated surfaces.
Refraction and prism
Snell's law, n₁ sin θ₁ = n₂ sin θ₂, governs bending at an interface; total internal reflection begins past the critical angle. Prism deviates light toward its base, and Prentice's rule predicts induced prism: P(Δ) = c(cm) × F(D).
Traps
- Using millimeters in F = 1/f (a 20 D lens has a 50 mm focal length, not 0.05 mm).
- Forgetting Prentice's rule requires centimeters of decentration.
- Adding prisms linearly when their bases point in different directions; perpendicular components must be resolved separately.
- Confusing chromatic aberration (measured by Abbe value; worse in polycarbonate and high index) with spherical aberration, coma, oblique astigmatism, and distortion.
Worked example
A −5.00 D lens decentered 4 mm induces P = 0.4 cm × 5.00 = 2.00Δ. For a minus lens, the base lies in the direction of decentration; for a plus lens the base points the opposite way. A +3.00 D lens decentered 3 mm gives 0.9Δ, base toward the decentration for plus.
Magnification has three components - power, shape, and position. Increasing vertex distance magnifies a plus lens and minifies a minus lens.