AP Physics 2 (Algebra-Based) — Geometric Optics Study Notes

Geometric optics

Branch of optics that models light as straight-line rays to predict image formation in mirrors and lenses, ignoring wave effects like diffraction and interference.

Ray

Idealized line indicating the direction that light energy propagates; used as a modeling tool rather than a physical “line of light.”

Diffraction

Wave effect where light spreads around edges or through small openings; neglected in geometric optics when objects/apertures are large compared with wavelength.

Interference

Wave effect from overlapping light waves that can produce bright/dark patterns; typically ignored in geometric optics.

Optical axis

Symmetry line of a mirror or lens used as the main reference line in ray diagrams.

Principal rays

A small, easy-to-trace set of rays that is sufficient to locate an image in a ray diagram.

Image (optics)

A location where rays actually converge (real) or appear to originate from when traced backward (virtual); not a physical object on a surface.

Real image

Image formed where light rays physically meet; can be projected onto a screen.

Virtual image

Image formed where rays only appear to meet when extended backward; cannot be projected onto a screen.

Intensity (light)

Measure of how much light energy passes through an area (brightness); higher where rays are more concentrated.

Reflection

“Bounce” of light off a surface; governed by the law of reflection.

Law of reflection

The incident angle equals the reflected angle, measured from the normal: θi = θr.

Normal line

Line perpendicular to a surface at the point where a ray hits; angles of incidence/reflection/refraction are measured from this line.

Plane mirror

Flat mirror that forms a virtual, upright image the same size as the object, located the same distance behind the mirror as the object is in front.

Concave mirror

Spherical mirror with reflective surface curving inward; can produce real or virtual images depending on object distance; f is positive (common convention).

Convex mirror

Spherical mirror with reflective surface bulging toward the object; for real objects produces virtual, upright, reduced images; f is negative (common convention).

Center of curvature

Center of the sphere of which a spherical mirror is a part.

Radius of curvature (R)

Distance from the mirror surface (vertex) to the center of curvature of a spherical mirror.

Focal point

Point where parallel rays converge after reflection/refraction (or appear to diverge from for diverging systems).

Focal length (f)

Distance from a mirror/lens to its focal point; for spherical mirrors (paraxial) f = R/2; sign depends on converging vs diverging element.

Paraxial approximation

Assumption that rays make small angles with the optical axis (stay near the axis), allowing simple mirror/lens relationships like f = R/2 for spherical mirrors.

Mirror equation

Relationship for spherical mirrors: 1/f = 1/do + 1/di.

Lateral magnification (m)

Image size ratio and orientation indicator: m = hi/ho = −di/do; negative means inverted, positive means upright.

Object distance (d_o)

Distance from the mirror/lens to the object (typically positive for a real object placed in front of the element under common AP conventions).

Image distance (d_i)

Distance from the mirror/lens to the image; sign indicates real vs virtual under the chosen convention (often + for real images, − for virtual images).

Sign convention (mirrors)

Common AP rule: f>0 concave, f

Refraction

Bending of light when it crosses a boundary between media because its speed changes.

Index of refraction (n)

n = c/v, where c is speed of light in vacuum and v is speed in the medium; typically n>1 because light slows in materials.

Snell’s law

Rule for refraction at a boundary: n1 sinθ1 = n2 sinθ2 (angles measured from the normal).

Apparent depth

Effect where objects underwater look shallower because refracted rays bend and the brain traces them back in straight lines, forming a virtual image closer to the surface.

Total internal reflection (TIR)

Complete reflection back into a higher-index medium when light attempts to go to a lower-index medium at an incident angle greater than the critical angle.

Critical angle (θ_c)

Incident angle (in higher-index medium) that produces a refracted angle of 90°; sinθc = n2/n1 (with n1>n_2).

Fiber optic cable

Technology that guides light by repeated total internal reflection in a high-index core surrounded by lower-index cladding.

Thin lens approximation

Assumption that lens thickness is negligible compared with object/image distances, so refraction is treated as occurring at a single plane.

Converging lens

Lens (typically convex) that brings parallel rays to a focus; f is positive in common sign conventions; can form real images when do>f and virtual when do<f.

Diverging lens

Lens (typically concave) that spreads parallel rays as if they originate from a focal point on the incoming side; f is negative; for real objects forms virtual, upright, reduced images.

Thin lens equation

Relationship for thin lenses: 1/f = 1/do + 1/di.

Sign convention (lenses)

Common AP rule: do>0 for real objects on incoming-light side; di>0 for real images on far side; d_i

Optical power (P)

Measure of lens strength: P = 1/f (with f in meters); converging lenses have positive power, diverging lenses have negative power.

Equivalent power (lenses in contact)

For thin lenses touching, powers add: Peq = P1 + P2 (equivalently 1/feq = 1/f1 + 1/f2).

Accommodation

Eye’s focusing process: changing lens shape (and thus focal length/power) to keep the image on the retina.

Near point

Closest distance at which the eye can focus clearly; often taken as about 25 cm for a typical young adult (varies and increases with age).

Far point

Farthest distance at which the eye can see clearly; for a normal eye it is effectively infinity.

Myopia (nearsightedness)

Vision defect where distant objects blur because relaxed eye focuses images in front of the retina; corrected with a diverging (negative power) lens.

Hyperopia (farsightedness)

Vision defect where near objects blur because eye would focus images behind the retina; corrected with a converging (positive power) lens.

Reading glasses

Converging lenses that create a virtual image of a nearby object at a farther distance (often the user’s near point), reducing accommodation demand.

Magnifying glass (simple magnifier)

Converging lens used with the object inside the focal length to produce a virtual, upright, magnified image.

Compound microscope

Two-converging-lens instrument: objective forms a real, inverted, magnified intermediate image; eyepiece magnifies it to create a final virtual image.

Objective lens

In a microscope/telescope, the first lens that forms a real image (often near its focal plane) of the object.

Eyepiece lens

Lens you look through; typically acts like a magnifying glass for the intermediate image, producing a final virtual image for comfortable viewing.