AP Physics 2 Unit 13 Review: Geometric Optics

12–15% of AP multiple choice
4 topics
AP exam review verified for 2027

Unit 13 is about how light rays reflect off mirrors and refract through lenses to form images. You use ray diagrams and two core equations, 1/so + 1/si = 1/f and M = -si/so, along with Snell's law n1 sin theta1 = n2 sin theta2, to solve problems about image location, size, and orientation.

Fiveable's AP Physics 2 Unit 13 review covers 4 topics, with guided practice questions for the unit.

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AP Physics 2 unit 13 topics

13.1

Reflection

Models light as a ray perpendicular to the wavefront. Applies the law of reflection (theta_i = theta_r) and distinguishes specular reflection from smooth surfaces and diffuse reflection from rough surfaces. Introduces ray diagrams as the core tool for geometric optics.

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13.2

Images Formed by Mirrors

Uses the mirror equation 1/so + 1/si = 1/f and magnification M = -si/so to find image location, size, and orientation for concave, convex, and plane mirrors. Ray diagrams with three principal rays confirm algebraic results.

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13.3

Refraction

Explains refraction as a speed change at a boundary, quantified by n = c/v. Applies Snell's law to predict bending direction and calculates the critical angle for total internal reflection when light moves from a denser to a less dense medium.

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13.4

Images Formed by Lenses

Applies the thin-lens equation and magnification to converging and diverging lenses. Converging lenses can form real or virtual images; diverging lenses always form virtual, upright, reduced images. Ray diagrams use three principal rays through the lens.

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Practice AP Physics 2 unit 13 questions

Try AP-style questions on unit 13, then use the review notes below for anything you miss.

AP Physics 2 unit 13 stimulus-based MCQs

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diagram

Stimulus-based practice question

Monochromatic light in air is incident on the flat surface of a semicircular glass block (n = 1.5) at the center of the flat face. The figure shows four rays—labeled A, B, C, and D—striking the curved surface from inside the glass at different angles of incidence: 10°, 30°, 42°, and 55° respectively.

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Question

The critical angle for this glass-air interface is approximately 42°. Which of the following correctly compares the behavior of Ray B (30°) and Ray D (55°) at the curved surface?

Ray B refracts into the air and bends toward the normal; Ray D undergoes total internal reflection and no light exits.

Ray B refracts into the air and bends away from the normal; Ray D also refracts into the air but at a very large angle near 90°.

Ray B refracts into the air and bends away from the normal; Ray D undergoes total internal reflection and no light exits.

Both Ray B and Ray D undergo total internal reflection because both rays originate inside the glass.

diagram

Stimulus-based practice question

A student sets up a laser and directs it at a flat mirror, as shown. The laser beam strikes the mirror surface at an angle of 30° measured from the mirror surface. The student claims the reflected beam makes an angle of 30° with the mirror surface on the other side of the normal.

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Question

Which option best evaluates the student's claim?

Incorrect, because reflection angles are measured from the surface, not the normal.

Incorrect, because the reflected ray makes 60° with the mirror surface.

Correct, because equal reflection angles are measured from the mirror surface.

Correct, because 30° from the surface means 60° from the normal.

AP Physics 2 unit 13 FRQs

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FRQ

Concave mirror image formation and location

1. A small object is placed in front of a concave spherical mirror on the principal axis. The mirror has focal length $f_m = 12.0\ \text{cm}$ and the object is placed a distance $d_{o,m} = 30.0\ \text{cm}$ from the mirror. A ray diagram is to be used with the approximation that light travels as rays and that the mirror is spherical with a small aperture. The mirror is initially in air $\left(n_{air} = 1.00\right)$ . A single incident light ray from the top of the object strikes the mirror at a point where the normal to the mirror surface makes an angle $\theta_i = 35.0^\circ$ with the incident ray, as shown in Figure 1.

Figure 1. Concave spherical mirror in air with an object on the principal axis and a single incident ray striking the mirror at a specified angle to the local normal.

Figure 2. Close-up of incidence at the concave mirror showing incident ray, local normal, and space to add the reflected ray.

Figure 3. Principal-axis ray diagram layout for a concave mirror with the object placed at 30.0 cm and focal point at 12.0 cm; space provided to mark the image location and orientation.

Complete the following tasks in Figures 2 and 3.

•

In Figure 2, Indicate the direction of the reflected ray from the mirror.

•

In Figure 3, Indicate the location of the image formed by the mirror and whether the image is upright or inverted.

ii.

The object has height $h_o = 3.00\ \text{cm}$ .

Derive an expression for the image distance $d_{i,m}$ and the image height $h_{i,m}$ formed by the mirror in terms of $f_m$ , $d_{o,m}$ , and $h_o$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 4. Mirror–lens–screen system with a plane-parallel slab (n_s = 1.50, thickness 4.00 cm) inserted between the mirror and lens at normal incidence.

Indicate whether a sharp image forms on the screen, forms in front of the screen, forms behind the screen, or no real image forms. The mirror remains in air. A thin converging lens of focal length $f_L = 20.0\ \text{cm}$ is placed on the principal axis a distance $L = 60.0\ \text{cm}$ to the right of the mirror, as shown in Figure 4. A plane-parallel slab with index of refraction $n_s = 1.50$ and thickness $t = 4.00\ \text{cm}$ is inserted between the mirror and the lens so that the rays pass through the slab at normal incidence. A screen is placed a distance $x_s = 30.0\ \text{cm}$ to the right of the lens.

Sharp image on the screen
Image forms in front of the screen
Image forms behind the screen
No real image forms

Justify your answer.

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FRQ

Concave mirror followed by a converging lens 40 cm away

2. A small object is placed on the principal axis of a concave spherical mirror. Light from the object reflects from the mirror and then passes through a thin converging lens that is placed on the same principal axis to the right of the mirror, as shown in Figure 1. Assume ideal ray behavior, paraxial rays, and that the surrounding medium is air.

Figure 1. Concave mirror–lens setup on a common principal axis (all distances along the axis, in cm).

Figure 2. Blank ray diagram template with mirror, lens, focal points, and object fixed to the same scale as Figure 1.

On Figure 2, draw two different principal rays from the top of the object that reflect from the concave mirror and then refract through the converging lens. Use the rays to locate and label the final image. Clearly indicate the direction of light propagation with arrows on the rays.

Derive an expression for the final image distance from the lens, $s_{i,L}$ , in terms of the object distance from the mirror $s_{o,m}$ , the mirror focal length $f_m$ , the lens focal length $f_L$ , and the mirror-to-lens separation distance $d$ . Begin your derivation by writing a fundamental physics principle or an equation from the reference information.

Figure 3. One-dimensional position axis along the principal axis for marking the mirror-only image and the final image.

Using your ray diagram from part A and the axis provided in Figure 3, mark and label (i) the location of the image formed by the mirror alone and (ii) the location of the final image formed after the light passes through the lens. For each image, state whether it is real or virtual and whether it is upright or inverted relative to the object.

Indicate whether the final image produced by the lens is located to the left of the lens, to the right of the lens, or at the lens. The object distance from the mirror is $s_{o,m}=30.0\ \text{cm}$ , the mirror focal length is $f_m=12.0\ \text{cm}$ , the lens focal length is $f_L=15.0\ \text{cm}$ , and the mirror-to-lens separation is $d=40.0\ \text{cm}$ .

Left of the lens
Right of the lens
At the lens

Then calculate the final image distance from the lens and briefly justify your indicated choice by referencing at least one feature of your answers to parts A, B, or C.

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FRQ

Image formation and focal length determination with converging lens

3. In Experiment 1, a student investigates image formation using a converging thin lens. The student is given a lens of unknown focal length f and is asked to experimentally determine f by measuring object and image distances for different object positions.

Describe a procedure for collecting data that would allow the student to determine the focal length f of the converging lens. In your description, include the measurements to be made. Include any steps necessary to reduce experimental uncertainty.

Describe how the collected data could be analyzed to determine f. Include references to appropriate equations and to relationships between measured quantities and the variables in those equations.

Figure 1. Thin-lens image-formation setup on an optical bench with a meter scale for measuring object distance dₒ and image distance dᵢ.

Figure 2. Graph grid for a straight-line plot to determine focal length f from thin-lens data.

Object distance, do (m)	Image distance, di (m)
0.30	0.60
0.35	0.47
0.40	0.40
0.45	0.36
0.55	0.30

In Experiment 2, the student places the object at several distances do from the lens and, for each trial, adjusts the screen to form a sharp real image. The student measures do and di for each trial. Table 1 contains the data collected.

Indicate two quantities, either measured quantities from Table 1 or additional calculated quantities, that could be graphed to produce a straight line that could be used to determine f.

Vertical axis: Horizontal axis:

ii.

On Figure 2, create a graph of the quantities indicated in part C(i) that can be used to determine f.

•

Use Table 2 to record the data points or calculated quantities that you will plot.

•

Clearly label the axes, including units as appropriate.

•

Plot the points you recorded in Table 2.

iii.

Draw a best-fit line for the data graphed in part C(ii).

Using the best-fit line described in part D, calculate an experimental value for the focal length f of the lens. A student uses the graph from part C to determine the focal length f. The student graphs $\frac{1}{d_i}$ (vertical axis) versus $\frac{1}{d_o}$ (horizontal axis) and draws a best-fit line. The best-fit line has y-intercept $b = 5.00\ \text{m}^{-1}$ .

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AP Physics 2 unit 13 practice test

A timed, AP-style test built only from unit 13 questions — multiple choice plus free response, scored with AI feedback. Use the standard format or build your own.

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Unit 13 review notes

13.1

The Ray Model and Reflection

A light ray is a straight line perpendicular to the wavefront, pointing in the direction of wave travel. In geometric optics, the wave nature of light is ignored, so rays travel in straight lines until they hit a surface. A laser is a practical example of a single coherent, monochromatic beam that can be modeled as a ray. When a ray strikes a surface, the law of reflection applies: the angle of incidence equals the angle of reflection, both measured from the normal to the surface at the point of contact.

Law of reflection: theta_i = theta_r; both angles measured from the normal, not the surface.
Specular reflection: Occurs at smooth surfaces where the normal direction is constant; produces clear, mirror-like images.
Diffuse reflection: Occurs at rough surfaces where the normal varies across the surface; light scatters in many directions.
Ray diagram: A diagram using straight lines to show the path of light before and after interacting with a surface or optical element.
Limits of the ray model: Rays cannot explain interference or diffraction; those phenomena require treating light as a wave (Unit 14).

Draw a ray hitting a flat surface at 35 degrees from the normal. Identify the incident ray, reflected ray, and normal, and label both angles.

Type	Surface	Reflected rays	Result
Specular	Smooth	All parallel	Clear image
Diffuse	Rough	Many directions	Scattered light, no clear image

13.2

Images Formed by Mirrors

Spherical mirrors form images by reflecting light according to the law of reflection. The focal length f equals half the radius of curvature R. The mirror equation 1/so + 1/si = 1/f relates object distance, image distance, and focal length. Magnification M = -si/so gives the ratio of image height to object height and indicates orientation. A positive si means a real image forms in front of the mirror; a negative si means a virtual image forms behind it. Ray diagrams use three principal rays to locate images: the ray parallel to the principal axis, the ray through the focal point, and the ray through the center of curvature.

Concave mirror: Converging mirror; parallel rays reflect toward the real focal point in front of the mirror. f is positive.
Convex mirror: Diverging mirror; parallel rays reflect as if from a virtual focal point behind the mirror. f is negative.
Mirror equation: 1/so + 1/si = 1/f; use consistent sign conventions (real images have positive si for mirrors).
Magnification: M = -si/so; negative M means inverted image, |M| > 1 means enlarged.
Plane mirror: Flat mirror with f at infinity; always forms an upright, virtual image the same size as the object, located as far behind the mirror as the object is in front.

An object is placed 30 cm in front of a concave mirror with f = 10 cm. Use the mirror equation to find si and M, then state whether the image is real or virtual and upright or inverted.

Mirror type	f sign	Image type (object outside f)	Image orientation	Image size
Concave (object outside f)	Positive	Real	Inverted	Varies with position
Concave (object inside f)	Positive	Virtual	Upright	Enlarged
Convex	Negative	Virtual	Upright	Reduced
Plane	Infinite	Virtual	Upright	Same size

13.3

Refraction and Total Internal Reflection

Refraction is the change in direction of a light ray as it crosses from one medium into another, caused by the change in the speed of light. The index of refraction n = c/v quantifies how much slower light travels in a medium compared to a vacuum. Snell's law n1 sin theta1 = n2 sin theta2 predicts the angle of refraction. When light moves from a medium with higher n to one with lower n, it bends away from the normal. If the angle of incidence exceeds the critical angle theta_c = sin^-1(n2/n1), no light is transmitted and total internal reflection occurs. This principle underlies optical fiber technology.

Index of refraction: n = c/v; higher n means slower light and more bending at a boundary.
Snell's law: n1 sin theta1 = n2 sin theta2; angles measured from the normal at the boundary.
Bending direction: Light bends toward the normal when entering a denser medium (higher n); away from the normal when entering a less dense medium.
Critical angle: theta_c = sin^-1(n2/n1); only defined when n1 > n2. At or beyond this angle, total internal reflection occurs.
Total internal reflection: All incident light reflects back into the denser medium; no refracted ray exits. Used in optical fibers.

Light travels from glass (n = 1.5) into air (n = 1.0) at an angle of incidence of 25 degrees. Use Snell's law to find the angle of refraction, then calculate the critical angle for this glass-air interface.

Condition	n1 vs n2	Ray bends	Possible outcome
Low to high n	n1 < n2	Toward normal	Refraction only
High to low n, below critical angle	n1 > n2	Away from normal	Refraction only
High to low n, at or above critical angle	n1 > n2	No transmitted ray	Total internal reflection

13.4

Images Formed by Lenses

Thin lenses form images by refracting light at two surfaces. A converging (convex) lens brings parallel rays to a real focal point on the transmitted side. A diverging (concave) lens spreads parallel rays as if they came from a virtual focal point on the incident side. The thin-lens equation 1/so + 1/si = 1/f has the same form as the mirror equation, and magnification M = -si/so applies with the same sign interpretation. For lenses, a positive si means a real image on the opposite side from the object; a negative si means a virtual image on the same side as the object. Ray diagrams use three principal rays: the ray parallel to the axis refracts through the far focal point, the ray through the near focal point emerges parallel, and the ray through the lens center passes undeviated.

Converging lens: Convex lens with positive f; can form real or virtual images depending on object position relative to f.
Diverging lens: Concave lens with negative f; always forms a virtual, upright, reduced image regardless of object position.
Thin-lens equation: 1/so + 1/si = 1/f; same form as the mirror equation but sign conventions differ for real/virtual images.
Magnification: M = -si/so; negative means inverted, positive means upright, |M| > 1 means enlarged.
Object at focal point: When so = f for a converging lens, refracted rays are parallel and no image forms (si approaches infinity).

An object is 20 cm from a converging lens with f = 15 cm. Find si and M. Is the image real or virtual? Upright or inverted?

Lens type	f sign	Object position	Image type	Orientation
Converging	Positive	Beyond f	Real	Inverted
Converging	Positive	Inside f	Virtual	Upright
Diverging	Negative	Any	Virtual	Upright

Key terms

Term	Definition
light ray	A straight line perpendicular to the wavefront of a light wave, pointing in the direction of travel. The fundamental model used throughout geometric optics.
ray diagram	A diagram using straight lines to show the path of light before and after interacting with a mirror or lens. Used to locate images and determine their properties.
concave mirror	A curved mirror that converges parallel incident rays toward a real focal point in front of the mirror. Focal length f is positive.
plane mirror	A flat mirror with a focal point at infinite distance. Always produces a virtual, upright image the same size as the object.
focal length	The distance from a mirror or lens to its focal point, represented by f. Equals half the radius of curvature for spherical mirrors.
magnification	M = -si/so; the ratio of image height to object height. Negative M indicates an inverted image; \|M\| > 1 indicates an enlarged image.
image	The optical reproduction of an object formed by a mirror or lens, described by position (si), size (M), orientation (upright or inverted), and type (real or virtual).
inverted image	An image that is flipped relative to the object, indicated by a negative magnification M.
principal rays	Three specific rays used in ray diagrams to locate images: the ray parallel to the principal axis, the ray through the focal point, and the ray through the center of curvature (mirrors) or lens center (lenses).
converging lens	A thin convex lens with positive focal length that refracts parallel rays to converge at a real focal point on the transmitted side.
diverging lens	A thin concave lens with negative focal length that refracts parallel rays to diverge as if from a virtual focal point on the incident side. Always produces a virtual, upright, reduced image.
critical angle	The minimum angle of incidence (from the normal) at which total internal reflection occurs when light travels from a denser medium (higher n) into a less dense medium. theta_c = sin^-1(n2/n1).
coherent light	Light in which waves maintain a constant phase relationship, as produced by a laser. A laser beam is the standard example of a ray in geometric optics problems.

How to review unit 13

Topics students miss most

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13.4

Images Formed by Lenses

48%175 tries

13.3

Refraction

43%120 tries

13.1

Reflection

42%163 tries

Mistakes to avoid in Geometric Optics

Measuring angles from the surface instead of the normal

Both the law of reflection and Snell's law require angles measured from the normal to the surface, not from the surface itself. Measuring from the surface gives the complement of the correct angle and produces wrong answers.

Mixing up sign conventions for mirrors and lenses

For mirrors, a positive si means the image is in front of the mirror (real). For lenses, a positive si means the image is on the opposite side from the object (also real). Confusing these leads to incorrect real/virtual classifications.

Assuming a concave mirror always forms a real image

A concave mirror forms a virtual, upright, enlarged image when the object is placed inside the focal length (so < f). Always check object position relative to f before predicting image type.

Applying the critical angle formula in the wrong direction

Total internal reflection only occurs when light travels from a medium with higher n to one with lower n. The formula theta_c = sin^-1(n2/n1) is undefined when n2 > n1 because the argument exceeds 1.

Forgetting that a diverging lens always produces a virtual image

Unlike a converging lens, a diverging (concave) lens produces a virtual, upright, reduced image for any object position. Students sometimes try to find real images for diverging lenses, which is not physically possible for a single thin diverging lens with a real object.

Geometric Optics on the AP exam

Quantitative ray-tracing and equation problems

Expect problems that require you to apply the mirror equation or thin-lens equation to find image distance or focal length, then interpret the sign of the result to classify the image as real or virtual and upright or inverted. Magnification calculations often follow. These problems reward careful sign convention work more than formula recall.

Snell's law and multi-boundary refraction

Refraction problems frequently involve light crossing two or more boundaries, such as air to glass to water. You may need to apply Snell's law at each interface in sequence, or determine whether total internal reflection occurs at a given boundary. Explaining the physical reason for bending direction (speed change, index comparison) is a common reasoning task.

Qualitative ray diagram reasoning

Some questions ask you to sketch or interpret a ray diagram rather than calculate. You may need to predict how moving an object closer to or farther from a mirror or lens changes image size, location, or type, or explain why a convex mirror always produces a virtual image. Connecting diagram features to physical reasoning about converging and diverging rays is the key skill.

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Unit 13 printables

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Frequently Asked Questions

What's on the AP Physics 2 Unit 13 progress check (MCQ and FRQ)?

The AP Physics 2 Unit 13 progress check in AP Classroom includes both MCQ and FRQ parts drawn from all four unit topics: reflection, images formed by mirrors, refraction, and images formed by lenses. MCQ questions typically ask you to identify image properties or predict how changing a lens affects image location. FRQ parts ask you to draw ray diagrams, apply the thin-lens or mirror equation, and explain your reasoning. For matched practice before the progress check, visit /ap-physics-2-revised/unit-13.

How do I practice AP Physics 2 Unit 13 FRQs?

AP Physics 2 Unit 13 FRQs most often come from Images Formed by Mirrors and Images Formed by Lenses, so those two topics deserve the most FRQ practice. Question types include drawing ray diagrams for concave and convex mirrors or converging and diverging lenses, solving for image distance and magnification using the mirror or thin-lens equation, and explaining why an image is real or virtual. To practice, work through problems where you change object distance and predict how the image shifts, then write out your reasoning in full sentences the way the scoring guidelines expect. Find practice problems and study guides at /ap-physics-2-revised/unit-13.

How should I study AP Physics 2 Unit 13?

Start with reflection and the ray model before moving to mirrors and lenses, since each topic builds on the last. For each topic, sketch ray diagrams by hand until locating images feels automatic, then practice the mirror equation and thin-lens equation with numbers. A solid study plan looks like this: 1. Reflection (13.1): Review the law of reflection and practice tracing rays off flat and curved surfaces.
2. Images Formed by Mirrors (13.2): Draw ray diagrams for concave and convex mirrors, then solve mirror equation problems for real and virtual images.
3. Refraction (13.3): Work through Snell's law problems and understand total internal reflection.
4. Images Formed by Lenses (13.4): Repeat the ray diagram process for converging and diverging lenses, connecting results to the thin-lens equation. After each topic, do a short set of practice questions to catch gaps early. Since geometric optics is 12-15% of the AP exam, it's worth spending real time here. All study materials are at /ap-physics-2-revised/unit-13.

Ready to review Unit 13?Start with the notes, check the topic cards, and use the practice or resource links when they are available for this course.

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