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25.7 Image Formation by Mirrors

3 min read•june 18, 2024

Mirrors are fascinating optical devices that manipulate light to create images. From flat mirrors to curved ones, they play with to show us the world in new ways. Understanding how mirrors work is key to grasping the basics of .

This topic dives into the nitty-gritty of image formation by mirrors. We'll explore how different mirror shapes affect light rays, create various types of images, and learn the math behind it all. It's a reflection of the broader principles of light and optics.

Image Formation by Mirrors

Image formation in flat mirrors

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  • Light rays reflect off the mirror's surface maintaining equal angles between the incident ray and the reflected ray relative to the surface normal (perpendicular line to the surface)
  • The is equal to the
  • The reflected rays appear to originate from behind the mirror, creating a that cannot be projected onto a screen as light does not actually pass through the image location
  • The image formed by a flat mirror exhibits the following characteristics:
    • Upright orientation matching the object's vertical orientation
    • Equal size to the object with a 1:1 ratio
    • Laterally inverted appearance with left and right sides reversed (as if looking at your reflection)
    • Equidistant location behind the mirror compared to the object's distance in front of the mirror

Spherical mirror image diagrams

  • Concave mirrors have a reflecting surface that curves inward, acting as converging mirrors
    • Parallel light rays incident on a converge at the after reflection
    • Concave mirrors can form both real images (inverted and projectable on a screen) and virtual images (upright and not projectable) based on the object's position relative to the
      • Objects beyond the focal point form real, inverted, and smaller or larger images
      • Objects between the focal point and the mirror form virtual, upright, and magnified images
  • Convex mirrors have a reflecting surface that curves outward, acting as diverging mirrors
    • Parallel light rays incident on a diverge after reflection, appearing to originate from a virtual focal point located behind the mirror
    • Convex mirrors always form virtual, upright, and smaller (diminished) images compared to the object, regardless of the object's distance from the mirror (rearview mirrors in vehicles)

Calculations for spherical mirrors

  • (ff) represents the distance between the mirror's surface and the focal point
    • Concave mirrors have a positive , with the focal point located in front of the mirror
    • Convex mirrors have a negative focal length, with a virtual focal point located behind the mirror
  • The relates the focal length (ff), object distance (dod_o), and image distance (did_i): 1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
    • Solving this equation allows for the calculation of the image distance or object distance when the other values are known
  • The (RR) is twice the focal length: R=2fR = 2f, representing the radius of the imaginary sphere that the mirror's surface is a part of
  • (mm) quantifies the size relationship between the image and the object, calculated as the ratio of the image height (hih_i) to the object height (hoh_o) or the negative ratio of the image distance (did_i) to the object distance (dod_o): m=hiho=−didom = \frac{h_i}{h_o} = -\frac{d_i}{d_o}
    • A negative value indicates an inverted (upside-down) image
    • Magnification greater than 1 (∣m∣>1|m| > 1) signifies an enlarged image compared to the object
    • Magnification less than 1 (∣m∣<1|m| < 1) signifies a reduced image compared to the object (makeup mirrors)

Key concepts in optics for mirrors

  • The is an imaginary line passing through the and the mirror's vertex
  • The center of curvature is the center of the sphere of which the mirror is a part
  • occurs when light rays reflecting from different parts of a spherical mirror do not converge at a single focal point, affecting image quality

Key Terms to Review (29)

Center of Curvature: The center of curvature is the center of the sphere that forms the curved surface of a mirror. It is the point around which the mirror's surface is curved, and it is an important concept in the study of image formation by mirrors.
Concave Mirror: A concave mirror is a curved reflecting surface that is thinner at the edges and thicker at the center, forming a bowl-like shape. This type of mirror is commonly used in various optical applications due to its ability to converge light rays, making it an important concept in the study of image formation by mirrors.
Converging Mirror: A converging mirror is a type of concave mirror that has a curved surface that reflects light inwards, causing the light rays to converge or come together at a specific point. This type of mirror is often used in various optical devices and applications due to its ability to focus light.
Convex Mirror: A convex mirror is a type of curved mirror that has a surface that bulges outward, causing the reflected image to appear smaller and more distant than the object. This type of mirror is commonly used in various applications, such as in vehicles, security systems, and surveillance cameras, due to its ability to provide a wider field of view.
Diverging Mirror: A diverging mirror is a type of curved mirror that causes light rays to spread out or diverge, resulting in the formation of a virtual, upright, and smaller image of the object placed in front of it. This type of mirror is commonly used in various applications, including makeup mirrors, shaving mirrors, and some vehicle side-view mirrors.
Focal length: Focal length is the distance from the center of a lens to its focal point, where parallel light rays converge or appear to diverge. It determines the converging or diverging power of the lens.
Focal Length: Focal length is a measure of the distance over which a lens or mirror can focus parallel rays of light. It is a fundamental property that determines the magnification and image formation characteristics of optical devices, such as cameras, telescopes, and the human eye.
Focal point: The focal point is the specific point where light rays parallel to the principal axis converge after passing through a lens or reflecting off a mirror. It is crucial for understanding image formation in optical systems.
Focal Point: The focal point is the point at which light rays converge or diverge after passing through a lens or reflecting off a curved mirror. It is the location where an image is formed in an optical system.
Incident Angle: The incident angle is the angle at which a light ray or other wave strikes a surface. It is the angle between the incident ray and the normal (a line perpendicular to the surface) at the point of incidence. The incident angle is a crucial parameter in the study of image formation by mirrors, as it determines the behavior of the reflected light.
Intensity reflection coefficient: The intensity reflection coefficient is a measure of the fraction of incident acoustic wave intensity that is reflected at the boundary between two different media. It is a dimensionless quantity and ranges from 0 to 1.
Lateral Inversion: Lateral inversion is a phenomenon that occurs when an image is flipped horizontally, resulting in a mirrored or reversed representation of the original object. This concept is particularly relevant in the context of image formation by mirrors, where the reflected image can exhibit this lateral inversion effect.
Law of Reflection: The law of reflection states that when a ray of light reflects off a surface, the angle of reflection is equal to the angle of incidence. This principle governs the behavior of light when it interacts with reflective surfaces and is a fundamental concept in understanding the formation of images by mirrors.
Magnification: Magnification is the measure of how much larger or smaller an image is compared to the object itself. It is given by the ratio of the image height to the object height.
Magnification: Magnification is the process of enlarging the apparent size of an object or image, making it appear larger than its actual size. This concept is crucial in understanding the formation of images by various optical devices, such as lenses, mirrors, microscopes, and telescopes.
Mirror Equation: The mirror equation is a fundamental relationship that describes the formation of images by curved mirrors. It is a mathematical expression that connects the object distance, image distance, and focal length of a mirror, allowing for the prediction and analysis of the characteristics of the resulting image.
Optics: Optics is the branch of physics that deals with the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. This field encompasses various phenomena such as reflection, refraction, dispersion, and the formation of images. Understanding optics is essential for explaining how light travels, how we perceive images, and how optical devices function.
Plane Mirror: A plane mirror is a flat, smooth reflective surface that produces an image of an object by reflecting light. It is a fundamental optical device used in various applications, including mirrors in everyday life, telescopes, and other optical instruments.
Principal Axis: The principal axis of a mirror is the central line or axis of symmetry that passes through the center of curvature of the mirror. It is the primary axis along which the mirror's optical properties are defined and image formation occurs.
Radius of curvature: The radius of curvature is the distance from the center of a circular path to any point on the path. It is used to describe the size of the circle in uniform circular motion.
Radius of Curvature: The radius of curvature is a measure of the curvature of a curve or surface at a specific point. It represents the radius of the circular arc that best approximates the curve or surface at that point. This concept is particularly important in the study of mechanics, optics, and other physical phenomena.
Ray Tracing: Ray tracing is a rendering technique used in computer graphics and optics to simulate the path of light through a scene. It involves tracing the trajectory of light rays as they interact with various objects, reflecting, refracting, and absorbing light to produce a realistic image.
Real image: A real image is formed when light rays converge at a point after passing through a lens or reflecting from a mirror. It can be projected onto a screen as the light actually passes through the image location.
Real Image: A real image is a type of image that is formed by the actual convergence of light rays from an object. It can be captured on a screen or photographic film and is considered a true representation of the object being imaged.
Reflection: Reflection is the change in direction of a wave, such as light or sound, when it encounters a boundary or surface. It is a fundamental concept in physics that describes how waves interact with different media and surfaces, leading to various phenomena observed in the physical world.
Reflection Angle: The reflection angle is the angle at which a light ray reflects off a surface, measured relative to the normal (perpendicular) line of the surface. It is a fundamental concept in the study of image formation by mirrors, a key topic in introductory college physics.
Spherical aberration: Spherical aberration occurs when light rays that strike a spherical mirror or lens near the edge focus at different points than those that strike closer to the center, resulting in a blurred image. This optical distortion arises because spherical surfaces do not converge light to a single focal point, causing images to appear fuzzy or out of focus, especially at the periphery. Understanding this phenomenon is crucial in analyzing how mirrors and lenses create images and how various optical aberrations can affect visual clarity.
Virtual image: A virtual image is an image formed by rays that appear to converge but do not actually meet. It cannot be projected onto a screen because the light rays only seem to come from the image location.
Virtual Image: A virtual image is an image that appears to exist in a different location than the actual object, but does not physically exist in that location. It is an image that is formed when light rays diverge or appear to diverge from a point, but do not actually intersect at that point.
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