Unit 13 · Geometric Optics

Light ray (ray model) ● (core concept) — A straight line perpendicular to the light wave's wavefronts, pointing in the travel direction. Rays predict light's behavior in geometric optics, where the wavelength is negligible — but they cannot explain interference or diffraction, which need the wave model.

Law of reflection ● (core concept) — θ_incident = θ_reflected: the angle between the incoming ray and the surface normal equals the angle between the outgoing ray and the normal.

Diffuse reflection ● (core concept) — Reflection from a rough surface, where the normal varies point to point so light scatters in many directions.

Specular reflection ● (core concept) — Reflection from a smooth surface, where the normal is nearly constant so light reflects uniformly in one direction (mirror-like).

Normal (line) ○ — The line perpendicular to a surface at the point where a ray strikes it. Angles of incidence, reflection, and refraction are all measured from the normal.

Focal point (mirrors) ● (core concept) — The point where rays parallel to the principal axis converge after reflection (concave/converging mirror) or appear to diverge from behind the mirror (convex/diverging mirror). A plane mirror's focal point is at infinity. For a spherical mirror, f ≈ R/2, halfway between the surface and the center of curvature.

Real image (mirror) ● (core concept) — An image formed when reflected rays actually intersect at a common point. It can be projected on a screen.

Virtual image (mirror) ● (core concept) — An image formed when reflected rays diverge so they only appear to come from a common point behind the mirror. It cannot be projected on a screen.

Mirror equation ● (core concept) — 1/s_i + 1/s_o = 1/f: relates image distance s_i, object distance s_o, and focal length f. Locations follow sign conventions measured from the mirror; a plane mirror gives s_i = s_o (image as far behind as the object is in front).

Magnification (mirrors and lenses) ● (core concept) — |M| = |h_i/h_o| = |s_i/s_o|: the ratio of image size to object size, also given by the ratio of image and object distances. |M| > 1 means enlarged, |M| < 1 means reduced.

Principal rays (mirrors) ● (core concept) — The three standard rays used in ray diagrams: (1) parallel to the principal axis, reflecting through (or as if from) the focal point; (2) striking the mirror's center, reflecting symmetrically; (3) passing through (or toward) the focal point, reflecting parallel to the axis. Mirror images can be upright or inverted, real or virtual, reduced, enlarged, or same-size.

Plane mirror ● (core concept) — A flat mirror whose focal point is at infinity. It forms a virtual image as far behind the mirror as the object is in front (s_i = s_o), upright and the same size as the object.

Concave mirror ● (core concept) — A converging mirror, curved inward like the inside of a bowl. Parallel rays reflect through its focal point (f ≈ R/2 in front of the mirror); it can form real or virtual images depending on object position.

Convex mirror ● (core concept) — A diverging mirror, curved outward. Reflected rays diverge as if from a focal point behind the mirror; it always forms a virtual, upright, reduced image.

Principal axis ○ — The straight line through the center of curvature (mirrors) or the centers of the lens surfaces, used as the reference line for ray diagrams and distance measurements.

Refraction ● (core concept) — The bending of a light ray as it passes from one medium into another, caused by the change in the speed of light in the new medium.

Index of refraction ● (core concept) — n = c/v: inversely proportional to the speed of light in the medium. Larger n means slower light and stronger bending.

Snell's law ● (core concept) — n₁sinθ₁ = n₂sinθ₂: relates the angles (measured from the normal) and indices on the two sides of an interface. Entering a higher-n medium bends the ray toward the normal; entering a lower-n medium bends it away. At normal incidence there is no bending.

Total internal reflection ● (core concept) — When light travels from a higher-index medium toward a lower-index one, beyond the critical angle all light reflects and none transmits. At the critical angle the refracted ray travels along the surface (refraction angle 90°); sinθ_c = n₂/n₁.

Critical angle ● (core concept) — The incidence angle (for light going from higher to lower index) at which the refracted ray travels along the surface — refraction angle 90°. Beyond it, total internal reflection occurs. sinθ_c = n₂/n₁.

Focal point (lenses) ● (core concept) — Rays parallel to the principal axis converge to the focal point on the far side of a thin convex (converging) lens, and diverge as if from the focal point on the near side of a thin concave (diverging) lens. A lens has a focal point on each side.

Real image (lens) ● (core concept) — An image formed when refracted rays actually intersect at a common point on the far side of the lens.

Virtual image (lens) ● (core concept) — An image formed when refracted rays diverge so they only appear to come from a common point on the same side as the object.

Thin-lens equation ● (core concept) — 1/s_i + 1/s_o = 1/f: relates image distance (from the lens midline), object distance, and focal length, with sign conventions measured from the lens.

Principal rays (lenses) ● (core concept) — The three standard rays: (1) parallel to the principal axis, refracting through (or as if from) the focal point; (2) through the lens center, continuing straight; (3) through (or toward) the focal point, refracting parallel to the axis. Lens images can be upright or inverted, real or virtual, reduced, enlarged, or same-size.

Converging lens ● (core concept) — A convex (thicker in the middle) thin lens that brings parallel rays to a focal point on the far side. It can form real or virtual images depending on object position.

Diverging lens ● (core concept) — A concave (thinner in the middle) thin lens that spreads parallel rays as if from a focal point on the near side. It always forms a virtual, upright, reduced image.