Optical Principles and Geometric Optics
This domain tests whether you can move fluently between vergence, the thin-lens relationship and the physical behaviour of light without sign errors. Items are usually short calculations dressed in clinical language.
Core relationships
- Snell's law: n₁ sin θ₁ = n₂ sin θ₂; critical angle θc = arcsin(n₂/n₁) for n₁ > n₂.
- Vergence L = n/l (dioptres, l in metres). Reduced vergence keeps the medium's index, not 1.00.
- Gaussian pair: L' = L + F, with lateral magnification m = L/L' = l'/l.
- Two thin lenses separated by d metres: F = F₁ + F₂ − d·F₁·F₂.
- Airy disc radius to first minimum: r = 1.22 λf/D; Rayleigh criterion separates two points.
Aberrations
The Seidel set (spherical aberration, coma, astigmatism, field curvature, distortion) plus longitudinal and transverse chromatic aberration. Higher-order terms are described by Zernike polynomials over a normalised pupil, with defocus and astigmatism dominating second order.
Worked example
An object is 40 cm in front of a +5.00 D thin lens in air. L = 1/(−0.40) = −2.50 D, so L' = −2.50 + 5.00 = +2.50 D and l' = +0.40 m: a real image 40 cm behind the lens. Magnification m = L/L' = −1.00, so the image is inverted and the same size. Move the object to 25 cm and L' = +1.00 D; the image now falls 1 m behind the lens and m = −4×.
Traps
Using 1.00 as the index for a lens sitting in aqueous or saline; dropping the negative sign for virtual images from diverging lenses; confusing the nodal point with the secondary principal plane when converting vertex to spectacle refraction; and quoting the Airy formula as a diameter rather than a radius.