Geometric Optics

Name: AP Physics 2: Algebra-Based Unit 5: Geometric Optics
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12–15% of the exam7 lessons · 96 min41 terms

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What this unit covers

The topics below follow the published Physics 2 course framework for Unit 5. This unit is worth 12–15% of the exam, so budget your time against that rather than against how long the unit takes to teach.

Reflection & refractionLenses & mirrorsRay diagramsTotal internal reflection

Lessons in this unit

Formulas in Unit 5

Law of reflection

θ_incidence = θ_reflection (both measured from the normal)

A ray hitting the mirror at angle θ to the surface makes an angle (90° − θ) to the normal, and reflects at that same angle on the other side of the normal.

Index of refraction and Snell’s law

n = c / v · n₁ · sinθ₁ = n₂ · sinθ₂

All angles are measured from the normal. The product n·sinθ is the same on both sides of the boundary, so a bigger n forces a smaller angle.

Mirror equation and magnification

1/f = 1/d_o + 1/d_i · m = − d_i / d_o

Sign conventions: d_i is positive for a real image (in front of the mirror), negative for a virtual image (behind). A positive m is upright; negative m is inverted; |m| > 1 is enlarged.

Thin-lens equation and magnification

1/f = 1/d_o + 1/d_i · m = − d_i / d_o

For a converging lens f > 0; for a diverging lens f < 0. A positive d_i is a real image on the far side of the lens; a negative d_i is a virtual image on the same side as the object.

The conventions

f > 0 converging (convex lens, concave mirror); f < 0 diverging (concave lens, convex mirror) · d_o > 0 for a real object · d_i > 0 REAL image (opposite side for a lens, in front for a mirror); d_i < 0 VIRTUAL · m = −d_i/d_o, so m < 0 is inverted

A negative image distance always means virtual, and a virtual image cannot be projected onto a screen.

Magnification

m = −d_i/d_o = h_i/h_o · sign gives orientation, magnitude gives size · overall for two elements: m_total = m₁ × m₂

Multiply, do not add. Two inversions give an upright final image, since two negatives multiply to a positive.

The critical angle

sin θ_c = n₂ / n₁, valid only when n₁ > n₂ · from Snell's law with a refraction angle of 90°

A larger index contrast gives a smaller critical angle, so more rays are totally reflected. Glass-to-air is about 42°; water-to-air about 49°.

Every term in Unit 5

All 41 terms we publish for Geometric Optics, with definitions. Reading them through is the fastest way to find the ones you cannot define — then drill those in cram mode until you can produce them without the prompt.

Index of refraction: n = c/v, always at least 1. Light slows in a denser medium while its frequency stays the same, so wavelength shortens.
Snell's law: n₁sin θ₁ = n₂sin θ₂. Light bends toward the normal entering a denser medium and away entering a less dense one.
Total internal reflection: Occurs only going from higher to lower index at angles above θ_c, where sin θ_c = n₂/n₁. This is the principle behind optical fibers.
Law of reflection: Angle of incidence equals angle of reflection, both measured from the NORMAL, not from the surface.
Dispersion: Index of refraction varies slightly with wavelength, so violet bends more than red — which is why a prism separates white light and why rainbows form.
Converging vs diverging lens: A convex lens has positive focal length and can form real images; a concave lens has negative focal length and forms only virtual, upright, reduced images.
Thin lens equation: 1/f = 1/d_o + 1/d_i. Positive d_i means a real image on the far side; negative means a virtual image on the same side as the object.
Magnification: M = −d_i/d_o = h_i/h_o. Negative M means inverted, and |M| > 1 means enlarged.
Real vs virtual images: Real images form where light actually converges and can be projected on a screen; virtual images only appear to come from a location and cannot.
Concave mirror: Converging, with positive focal length f = R/2. Produces a real inverted image when the object is beyond the focal point.
Convex mirror: Diverging, with negative focal length. Always produces a virtual, upright, reduced image — the reason it is used for wide-angle safety mirrors.
Ray diagram rules for a lens: A ray parallel to the axis refracts through the focal point; a ray through the center continues straight; a ray through the near focal point emerges parallel.
Sign conventions for lenses and mirrors: Object distance positive on the incoming side, image distance positive for a real image, focal length positive for converging. Most errors are sign errors.
Predicting image type without calculating: For a converging lens: object beyond 2f gives a real, inverted, reduced image; between f and 2f real, inverted, enlarged; inside f virtual, upright, enlarged.
Why a magnifying glass must be held close: Only when the object is inside the focal length does a converging lens produce an upright, enlarged virtual image.
Apparent depth: Refraction makes a submerged object appear shallower than it is, because rays bend away from the normal on leaving the water.
Fiber optics: Light entering at a shallow angle exceeds the critical angle at the core-cladding boundary and totally internally reflects along the fiber.
Chromatic aberration: Dispersion inside a lens focuses different colors at different points. Corrected by combining glasses with different dispersions.
Why the image of a half-covered lens is dimmer, not halved: Every point on the lens contributes rays to every image point, so blocking half reduces intensity but leaves the whole image visible.
Real image on a screen: Only real images can be projected. A virtual image cannot, because no light actually converges at its apparent location.
One equation for lenses and mirrors: 1/f = 1/d_o + 1/d_i. All the physics distinguishing cases lives in the SIGNS.
Sign of focal length: f > 0 for converging — convex lens, concave mirror. f < 0 for diverging — concave lens, convex mirror.
Negative image distance means virtual: No exceptions. A virtual image is where rays only appear to originate and cannot be projected on a screen.
Real versus virtual, physically: Real: rays actually converge, so a screen shows it — a projector or camera sensor. Virtual: nothing converges there, like your reflection in a flat mirror.
Three principal rays for a converging lens: Parallel in → through the far focus. Through the near focus → parallel out. Through the center → straight on. Any two locate the image.
Diverging optics always give the same image: Virtual, upright and reduced, whatever the object distance. No exceptions, which makes those questions quick.
Converging optics depend on position: Beyond f: real and inverted. Inside f: virtual, upright, enlarged — a magnifying glass. AT f: no image, since rays emerge parallel.
Two forms of magnification: m = −d_i/d_o = h_i/h_o. Sign gives orientation (negative is inverted); magnitude gives size.
Two-element systems multiply: m_total = m₁ × m₂, never added. Two inversions give an UPRIGHT final image.
Object distance for a second lens: The separation minus the first image distance. A negative result means the first image lies beyond the second lens — a virtual object, which the equation handles.
Two conditions for total internal reflection: Traveling from HIGHER index to LOWER index, AND above the critical angle. Both required — air into glass never qualifies.
Critical angle: sin θ_c = n₂/n₁, valid only when n₁ > n₂. A sine greater than 1 means you have the media reversed, and that impossibility is the physical answer.
Where the critical angle comes from: Snell's law with a refraction angle of 90° — the refracted ray grazing the boundary. Beyond it there is no solution, so all the light reflects.
Fiber optics and prisms: Total internal reflection is genuinely total, better than any mirror. Glass-to-air is about 42°, so a 45° prism face reflects everything.
Wavelength in a medium: λ_medium = λ_vacuum/n. Frequency is unchanged; the slower speed means a shorter wavelength.
Plane mirror image: Virtual, upright, the same size, and as far behind the mirror as the object is in front. Magnification is exactly +1.
Snell's law direction: Entering a denser medium bends the ray TOWARD the normal; entering a less dense one bends it away. This is what makes total internal reflection possible in only one direction.
Why light bends at all: Its speed changes: v = c/n. Frequency is fixed by the source, so a slower speed means a shorter wavelength inside the medium.
Concave versus convex mirror: Concave converges and has positive focal length; convex diverges and has negative focal length, always giving a virtual reduced image.
Focal length and radius of curvature: For a spherical mirror f = R/2. A flatter mirror has a longer focal length.
Two-element sequence: Solve the first element fully, then use its image as the object for the second. A negative object distance means a virtual object, which the equation handles.

What examiners penalize here

Memorize the plane-mirror image: virtual, upright, same size, equal distance behind. It is the reference point you compare curved-mirror and lens images against later in the unit.
Total internal reflection has two requirements, and both must hold: (1) light moving from high n to low n, and (2) an angle of incidence beyond the critical angle. If either fails, some light refracts through and it is not total.
Convex mirrors and diverging lenses share a signature: they always make virtual, upright, diminished images, no matter where the object is. Concave mirrors and converging lenses are the versatile ones whose image type depends on object position.
Learn the converging-lens cases by object position (beyond 2f, at 2f, between f and 2f, inside f) — the exam tests all four. And remember the shortcut: diverging lenses always give virtual, upright, diminished images, no computation needed.
State the sign convention you are using at the top of an optics free response. Rubrics accept either standard convention consistently applied, but they cannot award marks for a d_i whose sign meaning is unstated.
Solve two-element problems in strict sequence and write each intermediate d_i and m down. Rubrics award the first lens and the second lens separately, so a correct first stage earns credit even if the second goes wrong.
Before computing a critical angle, check that n₁ > n₂. If it is not, the correct answer is that total internal reflection cannot occur in that direction — which is worth stating explicitly rather than producing an impossible arcsine.

Practice Physics 2

Our practice bank is drawn from across the whole course rather than filtered to one unit, which is closer to how the exam asks anyway — it will not tell you which unit a question is testing.

194 practice questionsEvery one with a written explanation FRQ trainerWritten answers scored against the rubric Physics 2 study guideAll units, weights and score data in one place All 7 Physics 2 unitsThe full course

Questions about this unit

How much of the AP Physics 2: Algebra-Based exam is Unit 5?

Unit 5, Geometric Optics, is worth 12–15% of the Physics 2 multiple-choice section according to the published course framework. Across all 7 units that makes it a substantial share — heavier than an even split would give it.

What topics are covered in Physics 2 Unit 5?

Geometric Optics covers Reflection & refraction, Lenses & mirrors, Ray diagrams and Total internal reflection. We publish 41 terms with definitions for this unit, all of them on this page.

How should I study Physics 2 Unit 5?

Read the 7 lessons below first — about 95 minutes — then drill the 41 terms in cram mode until you can produce each definition from memory rather than just recognize it. Recognition is what makes a unit feel finished when it is not. Finish with practice questions and read the explanation for every one you get right by elimination as well as the ones you miss.

All 7 units of AP Physics 2: Algebra-Based

Unit names, topics and exam weights follow the published College Board course framework for AP Physics 2: Algebra-Based. AP® is a trademark registered by the College Board, which does not endorse this site.