The Part I optics formulas worth memorizing

Optics items on Part I reward speed. If you can set up a vergence problem in ten seconds, you bank time for the long condition-based items. These are the relationships worth knowing cold.

Vergence: the equation behind most lens problems

Vergence is the curvature of light in diopters: L = n / l, with l in meters and n the index of the medium. Light diverging from an object has negative vergence; light converging toward an image has positive vergence.

• Thin lens: V = U + P. An object 25 cm in front of a +6.00 D lens has U = −4.00 D, so V = +2.00 D and the image sits 50 cm behind the lens.
• Lateral magnification: m = U / V. A negative value means the image is inverted.
• Surface power: P = (n2 − n1) / r, with r in meters and positive when the center of curvature lies on the side light travels toward.
• Mirrors: the focal length is half the radius of curvature. Concave mirrors converge light and convex mirrors diverge it.

Refraction at a boundary

• Snell's law: n1 sin θ1 = n2 sin θ2.
• Critical angle: sin θc = n2 / n1, which only exists when light passes from a higher to a lower index. For crown glass (1.50) into air it is about 41.8°.
• Brewster's angle: tan θB = n2 / n1. At this angle reflected light is completely polarized; for glass in air it is about 56.3°.

Prism

• Prism diopter: 1Δ displaces light 1 cm at a distance of 1 m, which is about 0.57°.
• Thin prism in air: deviation = (n − 1) × apex angle, both in degrees.
• Prentice's rule: Δ = c × F, with decentration c in centimeters. Looking below the optical center, plus lenses induce base-up prism and minus lenses induce base-down prism.

Spectacles, contact lenses and vertex distance

• Effective power: Fc = F / (1 − dF), with d in meters, when a lens moves closer to the eye. A −8.00 D spectacle lens at 12 mm needs about −7.25 D at the cornea.
• Spherical equivalent: the sphere plus half the cylinder.
• Transposition: add the cylinder to the sphere, flip the sign of the cylinder and rotate the axis by 90°.
• Knapp's law: for an axial ametrope, a correcting lens at the eye's anterior focal point gives the same retinal image size as in a standard emmetropic eye.

Accommodation and near work

• Accommodative demand: 1 / distance in meters, so reading at 40 cm asks for 2.50 D.
• Tentative add: the working-distance demand minus half the amplitude of accommodation.
• Calculated AC/A: IPD in cm + (near phoria − distance phoria) / near demand, with eso positive and exo negative.
• Kestenbaum's rule: the starting add for 1M print is the reciprocal of the Snellen fraction, so 20/200 suggests +10.00 D.

Build the reflex

Recognizing a formula is not the same as using it under time pressure. Run ten optics questions in the bank in timed mode at Part I pace, and redo every miss until the setup feels automatic.