Plane Mirrors

• Light radiates in all directions from an object and we see only a small cone of light that enters our eyes.

• When light reflects off of a surface (mirror), our eyes do not detect the change in direction of the cone of light.

• A cone of light from the flame reflects off of the mirror. By extending the lines back behind the mirror, they will intersect at a point where our eyes perceive the candle to be.
• When we compare distances d_oand d_i we find that they are equal.
• The image from a plane mirror is as far behind the mirror (d_i) as the object is in front of the mirror (d_o).
• The characteristics of this image are:
  • Same size as the object
• Is vertically erect
• Is virtual

Curved Mirrors

Consider a Concave Mirror

• Parallel rays, parallel to the principal axis will converge at the focal point.
• Parallel rays not parallel to the principal axis will converge to a point just to the side of the focal point (called a focus).

• Objects that are not point sources of light will have rays incident on the mirror from many directions.
• These rays will then converge in various places, but will always be on one single plane (i.e. they will all be beside each other).
• Focal plane – The set of all foci including the principal focus.
  • These form a plane perpendicular to the principal axis.
  • A real image of the object forms on the focal plane.
• The closeness of the image to the mirror depends upon how far the object is away.
• Rules for determining the location of the image.
  1. An incident ray parallel to the principal axis is reflected through the principal focus (F).
  2. Any incident ray passing through the principal focus is reflected parallel to the principal axis
  3. An incident ray that passes through or when extended is through the center of curvature, will reflect back on the same line.
  4. The image is formed in the plane perpendicular to the principal axis where any two of these three rays intersect.

Summary of the characteristics of the image

• For rule 6, you can imagine that the object is a star. All rays come in parallel to the principal axis, and therefore reflect through the principal focus where the image of the star will be.
• For rule 4, since all reflected rays are parallel, and similarly for projected rays, no image either virtual or real will form.

Consider a Convex Mirror

• Use the same rules for locating the images.
• C, F, and images are all behind the mirror and are virtual.
• The image is always erect and smaller than the object.

• You should check to see if you can illustrate the other rules.

Equations for Curved Mirrors

• The following equations apply to curved mirrors.

• M = magnification, h_i = image height, h_o = object height, d_i = image distance, d_o = object distance, and f = focal length
• Proof of these equations:

Sign conventions

• All distances are measured from the vertex of a curved mirror for d_o and d_i.
• Distances of real objects and images are positive.
• Distances of virtual objects and images are negative.
• Object height and image height are measured from the principal axis and are positive if up and negative if down.
• Focal length is positive for converging (concave) mirrors and negative for diverging (convex) mirrors.
• Magnification (M) is positive if the image is erect and negative if the image is inverted.

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November 19, 2013