Concave (converging) and convex (diverging) mirrors differ in shape and how they form images. For concave mirrors, rays parallel to the principal axis reflect and meet at a real focal point in front of the mirror (13.2.A.1). Depending on object distance (use 1/si + 1/so = 1/f), a concave mirror can produce - real, inverted images (object beyond f), or - virtual, upright, enlarged images (object inside f). Magnification |M| = |hi/ho| = |si/so| tells you the size and orientation (13.2.A.8, 13.2.A.9). Convex mirrors reflect parallel rays so they appear to come from a focal point behind the mirror (13.2.A.2). They always produce virtual, upright, reduced images located behind the mirror; you never get a real image with a convex spherical mirror. For AP exam work: draw the three principal rays (parallel → focal, through center, through focal → parallel) on ray diagrams to identify image type, location, and magnification (13.2.A.9). For more examples and practice, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ), the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-13), and 1000+ practice questions (https://library.fiveable.me/practice/ap-physics-2-revised).

Real vs. virtual comes down to where the reflected rays actually go: - Real image: reflected rays physically intersect at a point in front of the mirror. You can project a real image onto a screen. (CED 13.2.A.5) - Virtual image: reflected rays diverge but, if you trace them backward, they appear to come from a common point behind the mirror. You can’t project a virtual image on a screen; you see it looking into the mirror. (CED 13.2.A.6) Quick rules you can use on the AP: - Plane mirrors: image is always virtual, upright, same size (focal point at infinity). (13.2.A.3) - Convex mirrors: always form virtual, reduced, upright images. (13.2.A.2) - Concave mirrors: can make either. If the object is farther than the focal length (so 1/si + 1/so = 1/f gives si > 0), the image is real and inverted; if the object is inside the focal length, the image is virtual and upright. (13.2.A.7, 13.2.A.4) Use ray diagrams with the three principal rays (parallel→focus, through center, through focal point) to check whether reflected rays actually meet (real) or only appear to meet behind the mirror (virtual). This is exactly what the exam expects—practice drawing and using the mirror equation. For a quick study guide and practice questions, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and extra problems (https://library.fiveable.me/practice/ap-physics-2-revised).

A concave (converging) mirror can make things look upside down when it forms a real image. If an object is placed farther from the mirror than the focal length, rays from each point on the object are reflected and actually intersect in front of the mirror at the image location (real image). Because those rays cross, the top of the object ends up at the bottom of the image—so the image is inverted. Use the mirror equation 1/si + 1/so = 1/f to find the image distance si; if si is positive (real image) and the magnification M = −si/so is negative, the image is inverted. Ray diagrams with the three principal rays (parallel→focal, through center, through focal→parallel) show this clearly. This is exactly what Topic 13.2 tests on the AP: identifying real vs. virtual, using the mirror equation, and deciding orientation. For a quick refresher, check the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and extra practice at the unit page (https://library.fiveable.me/ap-physics-2-revised/unit-13) or practice bank (https://library.fiveable.me/practice/ap-physics-2-revised).

The focal point of a mirror is the single location on the principal axis where rays that start parallel to that axis appear to meet after reflection. For a concave (converging) spherical mirror, parallel rays actually reflect and converge to a real focal point in front of the mirror (essential knowledge 13.2.A.1). For a convex (diverging) mirror, parallel rays reflect as if they originated from a virtual focal point behind the mirror (13.2.A.2). A plane mirror’s focal point is effectively at infinity (13.2.A.3). For spherical mirrors the focal length f ≈ R/2 (13.2.A.4), and image location depends on f and object distance via 1/si + 1/so = 1/f (13.2.A.7). On the AP exam you’ll use ray diagrams (principal rays: parallel→focal, center reflection, through focal→parallel) and the mirror equation to decide if images are real/virtual, upright/inverted, or magnified/reduced. For a quick refresher, check the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and more unit review at the Unit 13 page (https://library.fiveable.me/ap-physics-2-revised/unit-13).

Use the standard mirror sign convention: measure distances from the mirror along the principal axis. - so (object distance): positive when the object is in front of the mirror (real object). - si (image distance): positive if the image is formed in front of the mirror (real image—rays actually converge); negative if the image is behind the mirror (virtual image—rays only appear to diverge from that point). - f (focal length): positive for concave (converging) mirrors, negative for convex (diverging) mirrors. - Heights: hi positive for upright images, negative for inverted images. Use M = hi/ho = -si/so to get orientation and size. Quick examples: a real, inverted image from a concave mirror has so > 0, si > 0, f > 0 (M negative). A virtual upright image from a convex mirror has so > 0, si < 0, f < 0 (M positive). Always draw a ray diagram to check your signs—AP expects you to connect ray diagrams to the mirror equation (CED 13.2.A, see study guide: https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ). For extra practice, try problems at Fiveable’s practice page (https://library.fiveable.me/practice/ap-physics-2-revised).

Step-by-step: 1) Draw the mirror (concave, convex, or plane) and the principal axis. Mark the center of curvature (C) and focal point (F). For a spherical mirror f = R/2. 2) Place the object (arrow) upright at distance so/so from the mirror. 3) Draw the three principal rays from the object tip: - Ray 1: parallel to the principal axis → for a concave mirror reflects through F; for a convex mirror reflects as if it came from F behind the mirror. - Ray 2: through (or toward) the focal point → for concave reflects parallel to the axis; for convex, aim toward the focal point behind mirror and reflect parallel. - Ray 3: through the center of curvature (or hitting mirror center) → reflects back on itself (acts like a normal). 4) The image is where reflected rays actually meet (real image) or where backward extensions meet (virtual image). 5) Read off si and hi; use 1/si + 1/so = 1/f and |M| = |hi/ho| = |si/so| to classify size, orientation, and type per the CED. For guided practice and examples, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and try problems on Fiveable practice (https://library.fiveable.me/practice/ap-physics-2-revised). This matches AP expectations for ray diagrams and using the mirror equation.

Focal length and magnification are different kinds of things: - Focal length (f) is a fixed property of the mirror—where rays parallel to the principal axis meet (concave) or appear to come from (convex). For spherical mirrors f ≈ R/2, and for a plane mirror f is effectively infinite (CED 13.2.A.1–4). You plug f into the mirror equation 1/si + 1/so = 1/f to find image distance si (CED 13.2.A.7). - Magnification (M) describes how big the image is compared to the object: M = hi/ho = −si/so (the CED gives the magnitude |M| = |si/so|). It depends on the object and image distances, so it changes if you move the object even though f stays the same (CED 13.2.A.7, 13.2.A.8). On the AP exam you’ll use the mirror equation to get si from f and so, then use M to get image size/orientation (real/inverted vs. virtual/upright). For more review and worked examples see the topic study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and extra practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Because a convex (diverging) mirror always reflects incoming rays so they spread out, the reflected rays never actually meet in front of the mirror. Instead, if you extend those reflected rays backward behind the mirror they appear to come from one point (the focal point is behind the mirror per 13.2.A.2). By the CED definition, that is a virtual image: reflected rays diverge but appear to originate at a common point (13.2.A.6). You can also see this with the mirror equation: for a convex mirror f is negative, so solving 1/si + 1/so = 1/f gives si negative (image location behind the mirror), which indicates a virtual image. Ray diagrams using the three principal rays (parallel → appears to meet at focal point behind mirror, center-of-curvature ray behaves consistently, and ray aimed at the focal point reflects parallel) always produce an upright, reduced, virtual image for any real object position. For a quick review and practice problems on this topic, see the AP Physics 2 study guide (Topic 13.2) on Fiveable (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-13).

Think of mirrors by their shape: concave = "caves in" so it converges (reflects rays toward the axis), convex = "bulges out" so it diverges (reflects rays away so they appear to come from behind). Useful quick rules (use these on ray diagrams—CED 13.2.A and 13.2.A.9): - Parallel ray → focal point after reflection (concave: actually meets at focal point; convex: appears to come from focal point behind the mirror). - Ray through focal point → reflects parallel to the principal axis. - Ray to center of curvature → reflects back on itself (acts like normal there). Remember plane mirrors have focal point at infinity (CED 13.2.A.3). If reflected rays actually meet = real image; if they only appear to meet = virtual image (CED 13.2.A.5–A.6). For the exam practice ray diagrams, image-location/magnification use 1/si + 1/so = 1/f and |M| = |si/so| (CED 13.2.A.7–A.8). For a quick refresher and examples, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and tons of practice problems at Fiveable (https://library.fiveable.me/practice/ap-physics-2-revised).

As you move an object closer to a concave (converging) mirror, the image follows from the mirror equation 1/si + 1/so = 1/f and the magnification |M| = |si/so|: - If the object is beyond the center of curvature (so > 2f): image is real, inverted, smaller, and located between f and 2f. - Moving the object toward the mirror (decreasing so) moves the image farther from the mirror (si increases), so the image grows larger (|M| increases) and stays inverted while so > f. - When the object is at the focal point (so = f): si → ∞, so no image forms on a screen (rays become parallel). - If you move the object closer than the focal length (so < f): the image becomes virtual, upright, enlarged, and appears behind the mirror (si is negative by sign convention). For AP Physics 2, you should be able to use the mirror equation and ray diagrams (principal rays: parallel → focal, through center, through focal → parallel) to predict image type, location, size, and orientation (CED 13.2.A.5–9). For a quick refresher, check the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and more unit resources (https://library.fiveable.me/ap-physics-2-revised/unit-13). Practice problems are at (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of the focal point as “where parallel rays meet after reflection.” For a concave mirror parallel rays converge to a finite focal point; for a convex mirror they appear to diverge from a finite focal point behind the mirror. For a plane mirror, a ray parallel to the principal axis reflects parallel back—it doesn’t converge or diverge toward any finite point. So the point where all those reflected “parallel” rays would meet is infinitely far away. In other words the focal length f → ∞. You can also see this from the mirror equation 1/si + 1/so = 1/f: if f is infinite, 1/f = 0, so 1/si = −1/so and the image distance equals the object distance (virtual image same distance behind the plane mirror). This is exactly the CED statement (13.2.A.3). For a quick review, check the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and try practice problems at Fiveable (https://library.fiveable.me/practice/ap-physics-2-revised).

Think of the three principal rays as shortcuts you always draw to locate an image quickly on a ray diagram (this is exactly what the CED says: use these to find image location/type/size, 13.2.A.9.i). Simple rules: 1) Ray parallel to principal axis—draw it from the top of the object parallel to the axis. For a concave mirror it reflects through the focal point; for a convex mirror it reflects as if it came from the focal point behind the mirror. 2) Ray through (or toward) the focal point—draw it from the object through the focal point. For a concave mirror it reflects parallel to the principal axis; for a convex mirror, aim toward the focal point behind the mirror and it reflects parallel. 3) Ray through the center of curvature (the mirror’s center)—draw it toward the center; it reflects back on itself because it hits the mirror along the normal. Where the reflected rays actually intersect = real image. Where the extensions intersect behind the mirror = virtual image. Practice a couple of diagrams and use the mirror equation 1/si + 1/so = 1/f and magnification |M| = |si/so| to check (see Fiveable’s Topic 13.2 study guide for examples) (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ). For extra practice problems, check Fiveable practice sets (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the mirror equation to find the image distance, then relate that to size with the magnification formula. Steps: 1. Solve the mirror equation for si: 1/si + 1/so = 1/f → 1/si = 1/f − 1/so, so si = 1 / (1/f − 1/so). Use sign conventions: so is positive for real objects in front of the mirror; f is positive for concave, negative for convex. 2. Compute magnification M = hi/ho = − si/so. The negative sign means the image is inverted when M is negative; positive M means upright. (The CED gives the magnitude relation |M| = |hi/ho| = |si/so|.) 3. Interpret: |M| > 1 → image enlarged; |M| < 1 → reduced; M = −1 → same size inverted. Quick example: so = 30 cm, f = 20 cm (concave). 1/si = 1/20 − 1/30 = (3−2)/60 = 1/60 → si = 60 cm. M = −(60/30) = −2 → image inverted and twice as tall. For more review and AP-style practice, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and extra practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Whether an image is upright or inverted comes down to where the reflected rays actually go—real rays that converge vs. virtual rays that only appear to diverge—and that depends on the mirror type and object distance. Quick rules from the CED: - Real image (rays actually intersect): inverted. Happens with a concave (converging) mirror when the object is placed beyond the focal point. (13.2.A.5) - Virtual image (rays diverge and only appear to come from a point): upright. Happens with a plane mirror (image behind at same distance, upright) and with a convex (diverging) mirror (image always virtual and upright). Concave mirrors produce a virtual upright image only when the object is inside the focal length. (13.2.A.2–A.4, A.6) Use ray diagrams (the three principal rays: parallel→focal, through center, through focal→parallel) to see if reflected rays meet (real, inverted) or only appear to meet (virtual, upright)—that’s exactly what AP asks you to do (13.2.A.9). For a quick review, check the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ) and try practice problems (https://library.fiveable.me/practice/ap-physics-2-revised).

Use the mirror equation: 1/si + 1/so = 1/f. That relates object distance (so), image distance (si), and focal length (f). Also use magnification: M = hi/ho = −si/so to tell size and orientation. Quick rules you can use on the AP: - If so → ∞ (object far away), si ≈ f (image at focal point). - If so > f (outside focal point) for a concave mirror, si is positive → real, inverted image (e.g., so = 2f → si = 2f). - If so = f, the image is at infinity (rays parallel). - If so < f for a concave mirror, si is negative → virtual, upright, enlarged image located behind the mirror. - For a convex mirror f is negative; si is always negative → virtual, upright, reduced image (focal point behind mirror). Remember sign conventions matter (positive distances in front of the mirror, negative behind)—the AP expects you to apply them and use ray diagrams to check your answers (Topic 13.2, CED). For a quick refresher, see the Topic 13.2 study guide (https://library.fiveable.me/ap-physics-2-revised/unit-5/2-images-formed-by-mirrors/study-guide/INg7VTuspNL1m0MQ). For more practice, use the unit overview (https://library.fiveable.me/ap-physics-2-revised/unit-13) and the practice problem bank (https://library.fiveable.me/practice/ap-physics-2-revised).