Reflection

Summary

• Optics
  • Optics is the study of the nature and behavior of light
  • It can be divided into subdisciplines based on the type of model used to describe light.
    • In physical optics, light is assumed to behave like a classical wave.
    • In quantum optics, light is assumed to have both wave and particle properties.
      • Particles of light are called photons.
    • In geometric optics, light is assumed to travel in a definite direction with relatively little diffraction.
      • This behavior is known as rectilinear propagation.
      • The path of propagation of a light wave is a geometric ray.
        • The rays of geometric optics...
          • are perpendicular to the wave fronts of physical optics.
          • indicate the most probable path of the photons of quantum optics.
        • A ray is the path of least action connecting two points in space and is also...
          • the path of least time (the quickest path)
          • unique and therefore reversible
            • The principle of reversibility states that light will follow the exact same path if its direction of travel is reversed.
        • Rays are...
          • straight lines in empty euclidean space
          • geodesics in general relativistic space-time
        • The eye can see something only if a ray of light from the object reaches the eye.

  Rays vs. Wavefronts

• Interface
  • An interface is the boundary between...
    • two different media.
    • two regions of a medium with different characteristics such as...
      • density (which is often related to temperature)
      • concentration of solute (salinity, for example)
      • mechanical stress
  • When an incident ray meets an interface it will be partially
    • reflected
      • Reflected rays obey the law of reflection described in this section of this book.
    • transmitted
      • Transmitted rays obey Snell's law, which is described in the next section of this book.
    • absorbed
      • Absorbed rays obey the law of conservation of energy. (The energy of the ray is not destroyed, but changes form.)
  • Angles in geometric optics are measured with respect to a line normal to the interface.
    • The angle of incidence is the angle between the incident ray and the normal.
    • The angle of reflection is the angle between the reflected ray and the normal.
    • The angle of refraction is the angle between the transmitted ray and the normal.

  Rays and angles in geometric optics

• Reflection
  • Law of reflection: The angle of incidence equals the angle of reflection (θ_i = θ_r).
    • The law of reflection can be derived from the principle of least action.
  • Types of reflection
    • Regular reflection or spectral reflection
      • Incident rays of light are reflected in one direction according to the law of reflection.
      • Regular reflection occurs on smooth surfaces.
        • polished surfaces (metal, glass, etc.)
        • naturally flat surfaces (still water, black ice, etc.)
      • Parallel incident rays remain parallel after regular reflection (from a flat surface).
      • Regular reflection results in image formation.

      Parallel rays in, parallel rays out

    • Diffuse reflection
      • Incident rays of light are reflected in many directions with a statistically random distribution.
      • Diffuse reflection occurs on rough surfaces...
        • textured surfaces (brushed metal, crumpled aluminum foil, frosted glass, etc.)
        • naturally rough surfaces (paper, cloth, etc.)
        • multiple randomly oriented surfaces (foam, snow, etc)
        • subsurface irregularities (polished marble and a smooth coat of paint still reflect diffusely)
      • Parallel incident rays are not parallel after diffuse reflection.
      • Diffuse reflection is what makes most nonluminous objects visible.

      Parallel rays in, random rays out

    • Scattering
      • THIS NEEDS TO BE FIXED
      • Light is diffracted off of small particles so that the reflected waves are nearly spherical.
        • raindrops and smoke?
      • Light is absorbed by small particles and then emitted (effectively instantaneously) with a change in direction that is statistically random.
        • nitrogen molecules in the air?
• Optical Images
  • Every point on an object emits a set of diverging rays (called a ray bundle) in all possible directions.
  • If any of the rays in a bundle...
    • converge somewhere else, an in-focus real image of the original point will form at that location.
      • Real images can be captured on a screen.
    • can be traced backward to converge somewhere else, an in-focus virtual image of the original point will form at that location.
      • Virtual images cannot be captured on a screen.
• Plane Mirrors
  • The image formed in a plane mirror is...
    • the same distance behind the mirror as the object is in front (d_i = d_o)
    • the same size as the object; that is, neither magnified nor reduced (s_i = s_o)
    • upright or erect; that is, not upside down (as long as the mirror is vertical)
    • laterally inverted or perverted; that is, right handed objects produce left handed images (chirality is reversed)
    • virtual; that is, located at the apperent intersection point of the reflected rays