Geometrical optics and optical systems
Geometrical optics represents light by rays when wavelengths are much smaller than optical components. Ray models predict reflection, refraction, image position and instrument behavior.
Reflection and refraction
Angles are measured from the normal. Reflection obeys θr=θi. Refraction obeys n1 sinθ1=n2 sinθ2, with refractive index n=c/v. Entering a higher-index medium bends a ray toward the normal. Frequency stays fixed at a boundary; speed and wavelength change. From higher n to lower n, total internal reflection occurs for incidence above the critical angle, where sinθc=n2/n1.
Lenses, mirrors and images
For a thin lens in air, 1/f=1/do+1/di under a consistent sign convention, and transverse magnification m=hi/ho=−di/do. A converging lens has positive focal length and can make real inverted images for objects beyond f or virtual upright images inside f. A diverging lens makes a virtual upright reduced image for a real object. Spherical mirrors use a related equation; a concave mirror converges paraxial rays and a convex mirror diverges them.