Honors Physics
Table of Contents
Unit 16 Overview: Mirrors and Lenses
16.1 Reflection
16.2 Refraction
16.3 Lenses

Reflection and mirrors play a crucial role in optics. They govern how light bounces off surfaces, creating images we see daily. From flat mirrors to curved ones, understanding reflection helps us grasp everything from our morning routines to advanced telescopes.

The law of reflection forms the foundation, stating that the angle of incidence equals the angle of reflection. This principle applies to all mirrors, whether flat or curved. Curved mirrors, like concave and convex types, have unique properties that make them useful in various applications, from car mirrors to telescopes.

Reflection and Mirrors

Law of reflection for mirrors

  • Angle of incidence equals angle of reflection ($\theta_i = \theta_r$) measured from the normal line perpendicular to the mirror surface
  • Incident ray, reflected ray, and normal line all lie in the same plane ensures a predictable reflection pattern
  • Specular reflection occurs on smooth surfaces like mirrors where parallel rays reflect in a single outgoing direction (flat mirrors)
  • Diffuse reflection occurs on rough surfaces where parallel rays scatter in many different directions (paper, fabric)
  • Image formation relies on light rays from each point on the object reflecting off the mirror following the law of reflection
    • Reflected rays converge or appear to diverge from a single point, reconstructing the image (virtual images in plane mirrors)

Image calculations with curved mirrors

  • Concave (converging) mirrors reflect light inward, focusing parallel rays to a point called the focal point (F) located in front of the mirror (telescope mirrors)
    • Convex (diverging) mirrors reflect light outward, causing parallel rays to diverge with a focal point (F) located behind the mirror (car side mirrors)
  • Mirror equation $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$ relates focal length ($f$), object distance ($d_o$), and image distance ($d_i$)
  • Magnification equation $M = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$ compares image height ($h_i$) to object height ($h_o$)
  • Ray diagrams map image formation using the principal axis line perpendicular to mirror surface, focal point (F), and center of curvature (C)
    • Concave mirror ray tracing rules:
      1. Ray parallel to principal axis reflects through focal point
      2. Ray through focal point reflects parallel to principal axis
      3. Ray through center of curvature reflects back along the same path
    • Convex mirror ray tracing rules:
      1. Ray parallel to principal axis reflects as if from focal point
      2. Ray toward focal point reflects parallel to principal axis
      3. Ray toward center of curvature reflects back along the same path

Real vs virtual mirror images

  • Real images form when light rays actually converge, can be projected onto a screen, and appear inverted (concave mirrors beyond the focal point)
  • Virtual images form when light rays only appear to diverge, cannot be projected, and are upright (concave mirrors before focal point, plane mirrors)
  • Concave mirrors have diverse applications:
    1. Telescopes and satellite dishes utilize large focal lengths to magnify distant objects
    2. Makeup mirrors and dental mirrors have small focal lengths for detailed close-up views
    3. Car headlights and flashlights incorporate parabolic reflectors to collimate light into a beam
  • Convex mirrors expand the field of view but with reduced size:
    1. Rearview mirrors in vehicles provide a wider rear view to enhance safety
    2. Security mirrors in stores increase the surveillance area to deter theft
    3. Side mirrors on cars minimize blind spots by expanding the driver's view
  • Wave optics describes light behavior as electromagnetic waves, complementing geometric optics
  • Interference occurs when multiple light waves combine, resulting in constructive or destructive patterns
  • Polarization describes the orientation of light wave oscillations, which can be manipulated using polarizing filters
  • Refraction is the bending of light as it passes between media with different refractive indices
    • Snell's law quantifies the relationship between the angles of incidence and refraction at an interface

Key Terms to Review (22)

Refraction: Refraction is the bending of waves, such as light or sound, when they pass from one medium to another with a different density or refractive index. This change in direction occurs due to the difference in the speed of the wave as it moves through the two mediums.
Snell's Law: Snell's law is a fundamental principle in optics that describes the relationship between the angles of incidence and refraction when light passes from one medium to another with different refractive indices. It is a critical concept in understanding the behavior of electromagnetic radiation, reflection, refraction, and the functioning of lenses.
Interference: Interference is the phenomenon that occurs when two or more waves interact with each other, resulting in the creation of a new wave pattern. This interaction can lead to either constructive interference, where the waves reinforce each other, or destructive interference, where the waves cancel each other out.
Angle of Incidence: The angle of incidence is the angle at which a wave, such as light or sound, strikes a surface. It is the angle between the incident wave and the normal (perpendicular) to the surface at the point of incidence. This term is crucial in understanding the behavior of waves as they interact with various media and surfaces.
Angle of Reflection: The angle of reflection is the angle at which a wave or particle is reflected off a surface. It is a fundamental concept in the study of wave interference and reflection, and is closely related to the angle of incidence.
Polarization: Polarization refers to the orientation or alignment of the electric field component of electromagnetic radiation. It describes the direction in which the electric field oscillates as the wave propagates through space.
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 encounters a smooth, reflective surface.
Normal Line: The normal line is a line that is perpendicular to a surface at a given point. It is a fundamental concept in the study of reflection and refraction of light, as it helps determine the direction of the reflected or refracted light.
Specular Reflection: Specular reflection is a type of reflection where the angle of incidence of a light ray is equal to the angle of reflection, resulting in a mirror-like reflection. This phenomenon occurs when light interacts with a smooth, flat surface, such as a mirror or a still body of water.
Virtual Images: A virtual image is an image that is formed when light rays appear to diverge from a point, but do not actually pass through that point. It is an image that cannot be projected onto a screen, but can be perceived by the eye.
Diffuse Reflection: Diffuse reflection is a type of reflection that occurs when light strikes a rough or irregular surface, causing the reflected light to scatter in multiple directions. This is in contrast to specular reflection, where light is reflected at a single angle.
Concave Mirrors: A concave mirror is a type of curved mirror that has a reflective surface that curves inward, forming a concave shape. This type of mirror is commonly used in various optical applications, including telescopes, microscopes, and everyday items like makeup mirrors.
Convex Mirrors: A convex mirror is a curved reflecting surface that bulges outwards, causing light rays to diverge or spread apart after reflecting off the surface. This type of mirror is commonly used in various applications due to its ability to provide a wide field of view and a reduced image size.
Mirror Equation: The mirror equation, also known as the thin lens equation, is a fundamental relationship that describes the behavior of light when it reflects off a curved surface, such as a mirror. It establishes a connection between the object distance, image distance, and the focal length of the mirror, allowing for the prediction and analysis of the characteristics of the resulting image.
Magnification Equation: The magnification equation is a mathematical relationship that describes the ratio between the size of an image and the size of the object being imaged. It is a fundamental concept in optics and is used to analyze the properties of various optical systems, such as lenses and mirrors.
Focal Point: The focal point is the point at which light rays converge or diverge after reflecting off a surface or passing through a lens. It is the point where the image is in focus and where the intensity of light is greatest.
Principal Axis: The principal axis is a line or axis that passes through the center of a reflecting surface, such as a mirror or lens, and is perpendicular to the surface. It is a fundamental concept in the study of reflection and is essential for understanding the behavior of light when it interacts with curved surfaces.
Center of Curvature: The center of curvature is the point around which a curved surface or line is bent. It is the center of the circle that best fits the curved surface at a given point.
Ray Diagrams: Ray diagrams are graphical representations used to trace the path of light as it interacts with optical components, such as mirrors and lenses. They provide a visual tool for understanding the behavior of light and predicting the formation of images.
Parabolic Reflectors: Parabolic reflectors are concave surfaces that have a parabolic shape, designed to reflect and focus light or other forms of radiation. They are widely used in various applications, such as in telescopes, flashlights, and satellite dishes, to efficiently direct and concentrate the energy source.
Wave Optics: Wave optics is a branch of optics that deals with the behavior of light as a wave, focusing on phenomena such as interference, diffraction, and coherence. It provides a comprehensive understanding of how light interacts with various media and structures, going beyond the basic principles of geometric optics.
Real Images: A real image is an image formed by the convergence of light rays in a way that the image can be projected onto a screen or surface. Real images are formed when light rays from an object intersect at a point on the opposite side of a lens or mirror from the object.