Comprehensive Guide to Geometric Optics for AP Physics 2

Ray Model of Light

Assumes light travels in straight lines, changes direction only at boundaries, and rays are reversible.

Specular Reflection

Reflection off a smooth surface where rays remain parallel.

Diffuse Reflection

Reflection off a rough surface where rays scatter in multiple directions.

Law of Reflection

The angle of incidence equals the angle of reflection (θi = θr).

Normal Line

A perpendicular line to the surface at the point of incidence, used to measure angles in reflection.

Virtual Image

An image where light rays appear to diverge from; cannot be projected onto a screen.

Image Distance (d_i)

The distance from the mirror/lens to the image formed.

Object Distance (d_o)

The distance from the mirror/lens to the object being reflected or refracted.

Focal Point (f)

The point where parallel rays converge (in converging systems) or appear to diverge from (in diverging systems).

Index of Refraction (n)

A dimensionless number that describes how much light slows down in a medium, calculated as n = c/v.

Snell's Law

Describes the relationship between angles of incidence and refraction in different media (n1 sin θ1 = n2 sin θ2).

Total Internal Reflection (TIR)

Phenomenon where light is completely reflected within a medium, occurring when going from a higher index to a lower index medium.

Critical Angle (θ_c)

The minimum angle of incidence at which TIR occurs; calculated as sin θc = n2/n_1.

Real Image

An image formed by converging light rays that can be projected onto a screen.

Concave Mirror

A mirror that caves inward and can form real or virtual images depending on object distance.

Convex Mirror

A mirror that bulges outward; always forms virtual, upright, and reduced images.

Convex Lens (Converging)

A lens thicker in the center that converges light rays; can form real or virtual images.

Concave Lens (Diverging)

A lens thinner in the center that diverges light rays; always forms virtual, upright, and reduced images.

Ray Tracing Rules

Guidelines for drawing rays to locate images formed by mirrors and lenses.

Magnification (M)

The ratio of image height to object height; also calculated as M = -di/do.

Thin Lens Equation

An equation that relates focal length, object distance, and image distance: 1/f = 1/do + 1/di.

Object Distance Sign Convention

Positive for real objects; negative for virtual objects in multiple lens systems.

Image Distance Sign Convention

Positive for real images (mirror: front, lens: back); negative for virtual images (mirror: back, lens: front).

Focal Length Sign Convention

Positive for converging systems (concave mirror, convex lens); negative for diverging systems (convex mirror, concave lens).

Image Height Sign Convention

Positive for upright images; negative for inverted images.

Common Mistake: Normal Line Contusion

Students often measure angles relative to the surface instead of the normal line.

Sign Convention Errors

Forgetting that virtual images have a negative image distance (d_i).

Real vs. Virtual Geometry Mistake

Real images form on the opposite side of the object in lenses, but on the same side in mirrors.

Frequency Change during Refraction

Frequency remains constant when light changes medium, while speed and wavelength change.

Snell's Law Calculation

Ensure your calculator is in degrees mode for angle calculations unless specified otherwise.

TIR Conditions Reminder

TIR occurs only when transitioning from a higher to a lower index medium.

Refraction

The bending of light as it passes from one medium to another due to a change in speed.

Magnification Equation (M)

Relates image height to object height and distances: M = hi/ho = -di/do.

Plane Mirror Characteristics

Creates virtual, upright images with a magnification of 1 and distance di = -do.

Speed of Light in Vacuum (c)

Approximately 3.00 x 10^8 meters per second.

Light Rays

Lines that represent the path of light in geometric optics.

Image Formation

The process by which lenses and mirrors produce images through reflection or refraction.

Geometric Optics

A branch of optics that deals with light propagation in terms of rays.

Diverging Systems' Image Characteristics

Always yield virtual, upright, and reduced images.

Converging Systems' Image Characteristics

Can form real, inverted images or virtual, upright images depending on object distance.

Angle of Incidence

The angle between the incident ray and the normal line.

Angle of Reflection

The angle between the reflected ray and the normal line.

Refraction and Wavelength

As light enters a medium with a higher index of refraction, its wavelength decreases.