Optics and Ophthalmic Lens Theory
What this domain tests
Optics questions test whether you can move between power, focal length, vergence, and prism without losing sign conventions. The exam favors applied calculations and lens-effect reasoning over memorized formulas.
Core rules
- Focal length in meters is the reciprocal of power in diopters: F = 1/f. Converging lenses are positive; diverging lenses are negative.
- Vergence L = n/l, where l is distance from the lens in meters and n is refractive index. Light from a real object diverges and carries a negative sign in the common Cartesian convention.
- The thin-lens equation 1/f = 1/u + 1/v links object and image distances; use one consistent sign convention.
- Prism power in prism diopters is P = 100 × displacement(cm)/distance(cm), and Prentice's rule is P = cF, with c in centimeters.
- Surface power is F = (n2 − n1)/r, so a steeper curve or greater index difference increases surface power.
Worked example
A +5.00 D lens has focal length f = 1/5.00 = 0.20 m, or 20 cm. An object 50 cm in front of the lens has u = −0.50 m in Cartesian convention. Then 1/v = 1/f − 1/u = 5.00 − (−2.00) = 7.00, so v = 0.143 m, a real image about 14.3 cm behind the lens. If the eye looks 10 mm off center through this lens, Prentice gives 1.0 × 5.00 = 5.0 prism diopters.
Traps
Mixing centimeters and meters; dropping the minus sign on diverging vergence; treating prism diopters as degrees; and forgetting that lens power changes with index. Always carry units and check whether the image is real or virtual.