Images Formed by Mirrors - AP Physics 2

1. A toy is placed in front of a concave mirror at a distance less than the focal length. Which statement best describes the image? Use qualitative ray tracing: a ray parallel to the principal axis reflects through the focal point, and a ray aimed at the focal point reflects parallel to the axis. For this object position, the reflected rays diverge after reflection and do not meet in front of the mirror; the image is found only by extending the reflected rays backward behind the mirror. The image therefore cannot be projected onto a screen placed in front of the mirror.
   Answer: Virtual, upright, and larger than the object This question tests understanding of images formed by mirrors. When an object is placed inside the focal length of a concave mirror, rays parallel to the axis still reflect through the focal point, but now these reflected rays diverge rather than converge. To find the image, we must extend the diverging rays backward behind the mirror where they appear to originate. This creates a virtual image that cannot be projected on a screen. The virtual image appears upright and magnified compared to the object. Choice C incorrectly suggests a virtual inverted image, representing the misconception that virtual images can be inverted—virtual images are always upright. Remember that for concave mirrors, objects inside the focal length always produce virtual, upright, magnified images.
2. A 3.0 cm-tall object is placed in front of a concave mirror farther than $C$. A ray diagram shows the image forming between $F$ and $C$. Which statement best describes the image?
   Answer: Real, inverted, and smaller than the object This question tests understanding of images formed by mirrors. When an object is placed beyond the center of curvature C of a concave mirror, the converging reflected rays form a real image between F and C. The ray parallel to the principal axis reflects through F, while the ray through C reflects back on itself, and these rays meet closer to the mirror than the object position. Since the rays physically converge, the image is real and inverted, and because the image forms closer to the mirror than the object, the image is reduced in size. Choice A incorrectly states the image is virtual and upright, representing the misconception that images between F and C must be virtual. Apply ray tracing with principal rays to systematically determine where images form and their characteristics.
3. A 3.0 cm tall object is placed in front of a concave mirror between the mirror and $F$. Which statement best describes the image?
   Answer: Virtual, upright, and larger than the object This question tests understanding of images formed by mirrors. When an object is placed between a concave mirror and its focal point F, the reflected rays diverge after reflection and must be traced backward to locate the virtual image. This virtual image forms behind the mirror, is upright relative to the object, and is magnified (larger than the object). This is the principle behind magnifying mirrors used for detailed viewing. Choice C incorrectly suggests a virtual image smaller than the object, which represents the misconception that virtual images are always diminished. Use principal rays to verify that objects inside F produce virtual, upright, magnified images.
4. A small object is placed in front of a convex mirror. Which statement best describes the image size compared with the object?
   Answer: Smaller than the object This question tests understanding of images formed by mirrors. Convex mirrors have a diverging effect on light rays, causing reflected rays to spread out more than incident rays. When tracing principal rays, the parallel ray appears to come from the virtual focal point behind the mirror, while the ray aimed at the center reflects at a wider angle. These diverging rays, when traced backward, intersect closer to the mirror than the object distance, creating a diminished image. This size reduction occurs for all object positions because the virtual image always forms between the mirror surface and the focal point. Choice A incorrectly suggests magnification, representing the misconception that curved mirrors always magnify like magnifying glasses. Remember that convex mirrors always produce reduced images, making them useful for wide-angle viewing.
5. A car's passenger-side mirror is a convex mirror. A nearby motorcycle approaches the mirror along the principal axis. Which statement best describes the image in the mirror?
   Answer: Virtual and upright This question tests understanding of images formed by mirrors. Convex mirrors always produce virtual, upright, and diminished images regardless of object distance because their surface curves away from incoming light. When rays from the motorcycle strike the convex mirror, they reflect and diverge as if originating from a point behind the mirror between the surface and the virtual focal point. The diverging rays never physically meet, so the image is virtual and cannot be projected on a screen. Choice A (real and inverted) incorrectly applies concave mirror behavior to a convex mirror, a common misconception. Remember that convex mirrors, like those on vehicles labeled "objects in mirror are closer than they appear," always form virtual, upright, reduced images.
6. An object is placed between $F$ and $C$ of a concave mirror. A ray diagram is drawn using a ray parallel to the axis and a ray through $F$. The image formed is…
   Answer: real, inverted, and larger than the object This question tests understanding of images formed by mirrors. When an object is placed between F and C of a concave mirror, ray tracing shows that reflected rays converge beyond C. A ray parallel to the axis reflects through F, while a ray through F reflects parallel to the axis—these rays intersect beyond C to form a real image. This real image is inverted and larger than the object (magnified). Choice A incorrectly suggests a virtual image, but virtual images only form when objects are inside F. To solve these problems, always trace at least two principal rays to locate where they converge (real) or appear to diverge from (virtual).
7. A small candle is placed in front of a concave mirror at a distance greater than the focal length but less than twice the focal length. Which statement best describes the image? Assume the principal axis is horizontal and the candle is on the axis. Consider the standard ray-tracing rules: a ray parallel to the axis reflects through the focal point, and a ray through the center of curvature reflects back on itself. Based on this placement, the reflected rays converge on the same side of the mirror as the object, producing a definite image location in space rather than requiring back-tracing behind the mirror.
   Answer: Real, inverted, and larger than the object This question tests understanding of images formed by mirrors. When an object is placed between f and 2f from a concave mirror, rays parallel to the principal axis reflect through the focal point, while rays through the center of curvature reflect back on themselves. These rays converge beyond the center of curvature on the same side as the object, forming a real image that can be projected on a screen. The image is inverted (upside down) and magnified compared to the object. Choice C incorrectly suggests a real upright image, which represents the misconception that real images can be upright—real images from single mirrors are always inverted. To solve mirror problems systematically, trace at least two principal rays and find where they intersect (real) or appear to diverge from (virtual).
8. A 2.0 cm-tall candle is placed in front of a concave mirror, between the focal point $F$ and the center of curvature $C$. A ray diagram would show one ray parallel to the principal axis reflecting through $F$, and a second ray through $C$ reflecting back on itself. Which statement best describes the image?
   Answer: Real, inverted, and larger than the object This question tests understanding of images formed by mirrors. When an object is placed between the focal point F and center of curvature C of a concave mirror, the reflected rays converge in front of the mirror to form a real image. The ray parallel to the principal axis reflects through F, while the ray through C reflects back on itself, and these rays intersect beyond C. Since the rays actually converge (not just their extensions), the image is real and inverted, and because the object is closer to the mirror than the image, the image is magnified. Choice D incorrectly states the image is virtual and inverted, which represents the misconception that all magnified images must be virtual. To solve mirror problems systematically, trace the two principal rays and determine where they intersect to find image properties.
9. A small bulb is placed exactly at the focal point of a concave mirror. Which statement best describes the image? Using ray ideas, light rays from the bulb that strike the mirror reflect and emerge parallel to the principal axis. Because the reflected rays do not converge to a point at a finite distance in front of the mirror, no real image forms on a nearby screen. The image is effectively located at an infinite distance, corresponding to collimated reflected light rather than a finite image point.
   Answer: No finite image forms; the image is at infinity This question tests understanding of images formed by mirrors. When an object is placed exactly at the focal point of a concave mirror, incident rays reflect to become parallel to the principal axis. Since parallel rays never converge at a finite distance, no real image forms on a screen at any finite position. The reflected rays neither converge nor appear to diverge from a finite point, so the image is effectively at infinity. Choice A incorrectly suggests a finite real image, representing the misconception that objects at the focal point produce normal images—this is the unique position where no finite image forms. When analyzing mirror systems, recognize that placement at the focal point produces parallel reflected rays with no finite image.
10. A lab group uses a concave mirror to project an image onto a screen. The object is placed farther from the mirror than the focal length. Which statement best describes the projected image?
    Answer: Real and inverted This question tests understanding of images formed by mirrors. When an object is placed beyond the focal length of a concave mirror and an image appears on a screen, the image must be real because only real images can be projected (virtual images cannot be captured on screens). For any object distance greater than f, concave mirrors cause reflected rays to converge at a real image location, and ray diagrams show this image is always inverted relative to the object. The ability to project indicates converging light rays that physically meet at the image location. Choice A (virtual and upright) contradicts the fundamental property that virtual images cannot be projected on screens. When solving projection problems, immediately recognize that any image on a screen must be real, then use ray tracing to confirm it's inverted.
11. A student moves an object from far away toward a concave mirror until it is just inside the focal length. Which statement best describes the image at that final position? For object distances less than the focal length, reflected rays diverge and only appear to come from a point behind the mirror when extended backward. The image therefore cannot be projected on a screen in front of the mirror. Compared with the object, the apparent image is magnified due to the geometry of the diverging reflected rays.
    Answer: Virtual, upright, and larger than the object This question tests understanding of images formed by mirrors. When an object is positioned just inside the focal length of a concave mirror, rays parallel to the axis reflect through f, but since the object is closer than f, the reflected rays diverge. Extending these diverging rays backward reveals they appear to originate from a point behind the mirror, creating a virtual image. This virtual image is upright and magnified compared to the object. Choice A incorrectly suggests a real inverted image, showing the misconception that all concave mirror positions produce real images—objects inside f always produce virtual images. For concave mirrors, remember the critical boundary: objects beyond f yield real images, while objects inside f yield virtual, upright, magnified images.
12. A student stands in front of a convex mirror used as a hallway safety mirror. The student is several meters from the mirror, much farther than the focal length. Which statement best describes the image?
    Answer: Virtual and upright This question tests understanding of images formed by mirrors. Convex mirrors have a virtual focal point behind the mirror surface, causing all incident rays to diverge after reflection regardless of object position. When parallel rays from a distant object strike a convex mirror, they reflect and diverge as if coming from the virtual focal point behind the mirror. The brain interprets these diverging rays as coming from a virtual, upright, and diminished image located between the mirror surface and the focal point. Choice C (real and inverted) represents the misconception of confusing convex mirrors with concave mirrors, which can form real images. For any curved mirror problem, identify the mirror type first, then use ray diagrams to determine image properties.
13. An object is placed at the center of curvature of a concave mirror (twice the focal length from the mirror). Which statement best describes the image? Using standard ray diagrams, a ray parallel to the principal axis reflects through the focal point and a ray through the focal point reflects parallel to the axis. For this special placement, the reflected rays intersect at the same distance from the mirror as the object, implying a definite image location in front of the mirror. The image is formed by actual convergence of reflected rays.
    Answer: Real, inverted, and the same size as the object This question tests understanding of images formed by mirrors. When an object is placed at the center of curvature (2f) of a concave mirror, rays parallel to the axis reflect through f, while rays through f reflect parallel to the axis. These rays intersect exactly at the center of curvature on the same side as the object, creating a real image. The image has the same size as the object but is inverted (flipped upside down). Choice A incorrectly suggests a virtual upright image, representing the misconception that placement at 2f produces virtual images—objects beyond f always produce real images with concave mirrors. For special positions like 2f, memorize that the image forms at the same distance with equal size but inverted orientation.
14. An object is placed in front of a convex mirror at any finite distance. A ray diagram shows the image behind the mirror where ray extensions intersect. Which statement best describes the image?
    Answer: Virtual, upright, and smaller than the object This question tests understanding of images formed by mirrors. Convex mirrors are diverging mirrors that always produce the same type of image regardless of where the object is placed: virtual, upright, and smaller than the object. The reflected rays diverge outward, and only their backward extensions meet behind the mirror, creating a virtual image that appears closer to the mirror than the object. The diverging nature ensures the image is always diminished, and virtual images are always upright relative to the object. Choice D incorrectly suggests the image is inverted, representing the misconception that virtual images can be inverted. Remember that convex mirrors have consistent image characteristics: always virtual, upright, and reduced.
15. An object is placed in front of a concave mirror at a distance greater than the center of curvature $C$ (i.e., farther than $2f$). A ray diagram shows reflected rays converging between $F$ and $C$. Which statement best describes the image?
    Answer: Real, inverted, and smaller than the object This question tests understanding of images formed by mirrors. When an object is placed beyond the center of curvature C (farther than 2f) of a concave mirror, the reflected rays converge between F and C to form a real image. The ray parallel to the principal axis reflects through F, and the ray through C reflects back on itself, with their intersection occurring closer to the mirror than the object. Since the image forms where rays actually converge, it is real and inverted, and because the image distance is less than the object distance, the image is diminished. Choice C incorrectly states the image is real and upright, representing the misconception that real images can be upright. Use ray diagrams with principal rays to systematically determine image location and characteristics.
16. A small object is placed in front of a convex mirror at a distance much larger than the focal length. Which statement best describes the image?
    Answer: Virtual, upright, and smaller than the object This question tests understanding of images formed by mirrors. Convex mirrors always produce virtual images because the reflected rays diverge and only appear to meet behind the mirror when traced backward. These virtual images are always upright and smaller than the object, regardless of object distance. The diverging nature of convex mirrors makes them useful for wide-angle viewing in security mirrors and car side mirrors. Choice A incorrectly suggests a real, inverted image, which represents the misconception that all curved mirrors can produce real images like concave mirrors do. Remember that convex mirrors always produce virtual, upright, and diminished images for any object position.
17. A small object is placed at the center of curvature ($d_o=2f$) of a concave mirror. Which statement best describes the image formed?
    Answer: Real and inverted This question tests understanding of images formed by mirrors. When an object is placed at the center of curvature (2f) of a concave mirror, it lies at twice the focal length from the mirror surface. At this special position, a ray through the center of curvature reflects directly back on itself, while a ray parallel to the axis reflects through f, and these rays converge exactly at 2f on the same side as the object. The resulting image is real (formed by actual light convergence), inverted, and the same size as the object. Choice A (virtual and upright) represents the misconception of assuming images at 2f behave like those inside f. To remember image properties, use the rule that concave mirrors produce real, inverted images for all object positions beyond f.
18. An object is placed in front of a convex mirror and moved closer to the mirror while remaining in front of it. Which statement best describes the image?
    Answer: Virtual, upright, and smaller than the object This question tests understanding of images formed by mirrors. Convex mirrors always produce virtual images that are upright and smaller than the object, regardless of object position. As the object moves closer to a convex mirror, the image remains virtual and upright but becomes slightly larger, though still smaller than the object. The image always forms between the mirror surface and the focal point behind the mirror. Choice B incorrectly suggests a real, inverted image, which represents the misconception that moving objects closer can change a virtual image to a real one. Remember that convex mirrors only produce virtual, upright, diminished images.
19. A student places an object at the center of curvature ($d_o=2f$) of a concave mirror. Which statement best describes the image formed?
    Answer: Real and inverted This question tests understanding of images formed by mirrors. When an object is placed at the center of curvature (2f) of a concave mirror, all rays from a point on the object pass through the center and reflect back through the same point. The ray parallel to the axis reflects through the focal point, while the ray through the focal point reflects parallel, and both rays intersect at exactly 2f on the opposite side of the principal axis. This creates a real, inverted image that is the same size as the object. Choice A incorrectly identifies this as virtual and upright, showing confusion between object positions that produce real versus virtual images. Remember that the center of curvature is a special position where object and image distances are equal, producing same-sized but inverted images.
20. A coin is placed in front of a convex mirror at a distance comparable to the mirror's focal length. Which statement best describes the image? For a convex mirror, reflected rays always diverge, so the image is found by extending the reflected rays backward behind the mirror. The image therefore cannot be formed on a screen in front of the mirror. Regardless of the object's distance in front of a convex mirror, the image appears upright and reduced compared with the object.
    Answer: Virtual, upright, and smaller than the object This question tests understanding of images formed by mirrors. Convex mirrors cause all incident rays to diverge upon reflection, regardless of the object's position. The virtual focal point lies behind the mirror, and reflected rays appear to originate from points between the mirror surface and this virtual focal point. The image is always virtual (formed by backward ray extensions), upright, and smaller than the object. Choice B incorrectly suggests a real inverted image, demonstrating the misconception that convex mirrors can produce real images—they cannot because reflected rays always diverge. Remember that convex mirrors invariably produce virtual, upright, reduced images for all object positions.

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