Optics and Mirrors

Object Visualization

  • A freestanding object emits rays of light in all directions.
  • When your eyes encounter light rays that diverge from a point in space, you perceive an image of the object as if it were at that point in space.

Real & Virtual Image Formation

  • A lens or curved mirror can make rays diverge from other points in space.
  • When your eyes encounter light rays that diverge from a point in space, you perceive an image of the object as if it were at that point in space.
  • We’re dealing with spherical lenses and mirrors, whose surfaces are shaped as a section of a sphere of radius R.
  • The focal length of a spherical lens or mirror is half of R.
    • f = \frac{R}{2}

Qualitative Mirror Exploration

  • Using the Geometric Optics PhET simulation, the following explorations can be made:
    • What happens when the object crosses over the focal point of the mirror?
    • What happens when the object is placed at the focal point of the mirror?
    • Do the previous two answers differ for a concave vs. a convex mirror?
  • The orientation of the image flips.
  • The image appears on the other side of the mirror.

Quantitative Mirror Exploration

  • The focal length f, image distance di, and object distance do are related by the Newtonian Mirror Equation:
    • \frac{1}{do} + \frac{1}{di} = \frac{1}{f}
  • Magnification Equation:
    • M = \frac{hi}{ho} = - \frac{di}{do}
  • d_o will, in the Newtonian convention, always be positive.
  • Variable sign conventions:
    • M:
      • +: Upright, virtual image
      • -: Inverted, real image
    • d_i:
      • +: Image & object on different sides
      • -: Image & object on the same side
    • h_i:
      • +: Upright, real image
      • -: Inverted, virtual image

Drawing Ray Diagrams for Concave Mirrors

  • Steps:
    1. Draw the first principal ray:
      • Start at one point on the object (try the top), draw parallel to the optical axis, then from the reflective plane through the near focal point.
    2. Draw the second principal ray:
      • Start at the same point on the object, draw through the near focal point to the reflective plane, then parallel to the optical axis.
    3. Resolve the image at the point where the two principal rays cross.
      • This will form a real image.

Drawing Ray Diagrams for Convex Mirrors

  • Steps:
    1. Draw the first principal ray:
      • Start at one point on the object (try the top), draw parallel to the optical axis, then from the reflective plane as if it had come from the far focal point.
    2. Draw the second principal ray:
      • Start at the same point on the object, draw through the far focal point to the optical surface, then parallel to the optical axis.
    3. Resolve the image at the point where the two principal rays cross.

Real Image Formation

  • Real images are caused by rays that actually emerge from an actual point in space.
  • Concave mirrors form real images on the same side as the object.

Virtual Image Formation

  • Virtual images are caused by rays that do not actually emerge from a point in space.
  • Concave mirrors form virtual images on the opposite side as the object.
  • You can’t light anything on fire with a virtual image — you can’t even project it on a piece of paper!

Creating a Real Image of the Sun

  • Draw a ray diagram of sunlight reflecting off a concave mirror.