Geometrical and physical optics with explicit models
Optical calculations begin with a model, sign convention and consistent units. A diopter is a reciprocal meter in the usual thin-lens power model. A distance written in centimeters must be converted before it is inserted into a formula using meters. Real and virtual objects or images require the stated convention; a memorized sign without a diagram can produce a plausible but reversed result.
Refraction at a boundary follows the relation between index and angle measured from the normal. Use the indices appropriate to the wavelength and media. A critical-angle calculation applies when light passes from the higher-index medium toward a lower-index medium. If the required sine exceeds the allowed range in that model, there is no corresponding refracted ray. An angle measured from the surface cannot be substituted silently for one measured from the normal.
Thin-lens, surface and prism formulas are approximations with domains of use. A lensmaker calculation requires the chosen radius signs, surrounding medium and any thin-lens assumption. A simple prism deviation model uses small-angle conditions. Prentice’s rule relates decentration in centimeters and meridional power to prism diopters. Direction depends on lens sign, location of the viewing point and the convention, so magnitude alone is not a complete base-direction answer.
Physical optics adds wavelength, interference, polarization and diffraction. Light’s frequency remains unchanged at a stationary material boundary while wavelength changes with refractive index. Quarter-wave coating thickness is an optical-path design condition at a specified wavelength and incidence, not a guarantee of zero reflection across every angle and color. Diffraction resolution is a theoretical model affected by aperture; a human visual-acuity result also depends on the rest of the optical and neural system.
Check limiting behavior and scale. A stronger converging thin lens has a shorter positive focal length in the simple air model. Chromatic effects depend on dispersion as well as nominal refractive index. Keep significant figures and rounding separate from the underlying calculation, and compare all answer choices only after the units and signs are correct. Written models support optical reasoning but do not replace actual lens measurement, instrument calibration or a complete patient refraction.