Review AP Physics 2 Unit 13 to build fluency with the ray model of light, reflection from mirrors, refraction at boundaries, and image formation by lenses. This unit carries 12-15% of the exam and requires both diagram skills and quantitative problem-solving with the mirror and thin-lens equations.
Use the topic guides, practice questions, and FRQ practice available for all four topics to work through ray diagrams and equation-based problems.
Geometric optics treats light as traveling in straight lines called rays. This model is valid when the wave nature of light can be ignored, which is the case for reflection and refraction at surfaces but not for interference or diffraction (covered in Unit 14). Unit 13 applies the ray model to mirrors and lenses to predict where images form, what size they are, and whether they are real or virtual.
A light ray is a straight line perpendicular to the wavefront. The law of reflection states that the angle of incidence equals the angle of reflection, both measured from the normal. Specular reflection occurs at smooth surfaces; diffuse reflection occurs at rough surfaces where the normal direction varies.
Concave mirrors converge parallel rays to a real focal point; convex mirrors diverge them to a virtual focal point behind the mirror. The mirror equation 1/so + 1/si = 1/f and magnification M = -si/so determine image location and size. Sign conventions distinguish real from virtual images and upright from inverted orientations.
Refraction occurs because light changes speed at a boundary, quantified by the index of refraction n = c/v. Snell's law n1 sin theta1 = n2 sin theta2 predicts the bending direction. When light moves from a denser to a less dense medium at an angle exceeding the critical angle, total internal reflection occurs. Converging and diverging lenses use refraction to form images described by the same thin-lens equation form as the mirror equation.
Reflection and refraction both cause light to change direction, so the apparent position of an object seen through a mirror or lens differs from its actual position. This is the central insight of geometric optics: image location is determined by tracing rays through the optical system, not by assuming light travels in a straight line from object to eye.
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.
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.
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.
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.
This snapshot uses Fiveable practice activity to show where students tend to miss questions and which review moves are worth prioritizing first.
Across 582 multiple-choice practice attempts for this unit.
Practice activity included in this snapshot.
Across 4 scored free-response attempts for this unit.
Review Images Formed by Lenses with attention to how the concept appears in AP-style source and evidence questions.
Review Refraction with attention to how the concept appears in AP-style source and evidence questions.
Review Reflection with attention to how the concept appears in AP-style source and evidence questions.
Review Images Formed by Mirrors with attention to how the concept appears in AP-style source and evidence questions.
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.
| Type | Surface | Reflected rays | Result |
|---|---|---|---|
| Specular | Smooth | All parallel | Clear image |
| Diffuse | Rough | Many directions | Scattered light, no clear image |
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.
| 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 |
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.
| 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 |
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.
| 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 |
Try stimulus-based AP practice questions and written prompts after you review the notes.
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.
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.
1. A small object is placed in front of a concave spherical mirror on the principal axis. The mirror has focal length and the object is placed a distance 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 . 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 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.
The object has height .
Derive an expression for the image distance and the image height formed by the mirror in terms of , , and . 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 is placed on the principal axis a distance to the right of the mirror, as shown in Figure 4. A plane-parallel slab with index of refraction and thickness 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 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.
2. A narrow beam of red light (wavelength in air ) is modeled as a ray. The ray travels in air and strikes a flat plane mirror at point P. The mirror is oriented so that the normal at P is in the plane of the page. The incident ray makes an angle of with the normal. After reflecting from the mirror, the ray travels through air toward a transparent semicircular block of radius . The ray enters the block through the curved surface along a radius directed toward the center of curvature, so the ray is incident normally on the curved surface. The block has index of refraction . The ray then reaches the flat face of the block and emerges back into air. The reflected and refracted rays then pass through a thin converging lens of focal length . An object (a small arrow) of height is placed on the principal axis at a distance to the left of the lens, as shown in Figure 1.
Figure 1. Reflection from a plane mirror, refraction through a semicircular block, then imaging by a converging thin lens (all distances and angles labeled).
Figure dot. Ray diagram space for Part A (reflection at point P).
On the diagram provided (see Figure dot), draw and label the reflected ray from the plane mirror at point P. Clearly label the angle of incidence and the angle of reflection measured from the normal, and indicate their numerical values in degrees.
Derive an expression for the angle (measured from the normal to the flat face) at which the ray emerges into air from the flat face of the semicircular block in terms of and the angle at which the ray inside the block strikes the flat face. Begin your derivation by writing a fundamental physics principle or an equation from the reference information.
Figure 2. Principal-axis ray diagram workspace for a thin converging lens (f = 10.0 cm) with object at d_o = 15.0 cm.
On the axes provided (see Figure 2), sketch a ray diagram for the converging lens showing at least two principal rays from the top of the object that pass through the lens and form the image. Draw and label the image, and indicate whether the image is real or virtual and whether it is upright or inverted. Assume the ray that reaches the lens can be treated as part of the light from the object. The lens is thin and in air, and the object is on the principal axis.
Indicate whether the image distance for the lens is greater than, less than, or equal to . Use , , and .
given_values:
Briefly justify your answer by referencing at least one feature of your answers to parts B or C, and by using the thin lens equation qualitatively or quantitatively.
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:
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.
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 (vertical axis) versus (horizontal axis) and draws a best-fit line. The best-fit line has y-intercept .
| 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. |
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.
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.
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.
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.
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.
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.
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.
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.
Open the individual guides for Unit 13 when you want a closer review of one topic.
browse guidesUse AP-style practice after you review the notes so you can check what you understand.
start practicePractice free-response reasoning and compare your answer with scoring guidance.
practice FRQsUse unit cheatsheets for a quick visual review after you work through the notes.
open cheatsheetsEstimate your broader AP score goal after you review the course and exam format.
open calculatorAP Physics 2 Unit 13 covers 4 topics in geometric optics: **13.1 Reflection**, **13.2 Images Formed by Mirrors**, **13.3 Refraction**, and **13.4 Images Formed by Lenses**. You'll use the ray model of light to trace how light bounces off mirrors and bends through lenses to form real and virtual images. See all four topics at /ap-physics-2-revised/unit-13.
AP Physics 2 Unit 13 makes up 12-15% of the AP exam, making geometric optics one of the heavier-weighted units. That weight comes from four topics: reflection, images formed by mirrors, refraction, and images formed by lenses. Expect both multiple-choice and free-response questions that test your ability to draw ray diagrams and apply the mirror and lens equations.
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.
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.
The best place to find AP Physics 2 Unit 13 practice questions, including multiple-choice and practice test sets, is /ap-physics-2-revised/unit-13. That page has resources covering all four topics: reflection, images formed by mirrors, refraction, and images formed by lenses. For MCQ practice, focus on questions that ask you to compare image types across different mirror and lens setups, since those are the most common question formats on the actual exam.
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.