PreAP Physics

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Pre-AP Physics

• Chapter 14
• -3 Curved Mirrors
• J. Mann
• March 23, 2006

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Concave Spherical Mirrors

• A spherical mirror with light reflected from its
  silvered, concave surface (the inner surface) is
  called a concave spherical mirror.
• This type of mirror is used whenever a magnified
  image of an object is desired

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Radius of Curvature

• Where the image appears and how large it appears
  depends of the mirror curvature.
• Mirror curvature is dependant on its radius of
  curvature, R, which is the distance from the
  mirrors surface to the center of curvature, C.

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Other Parameters

• The point on the mirror's surface where the
  principal axis meets the mirror is known as the
  vertex, A. The vertex is the geometric center of
  the mirror.
• Midway between the vertex and the center of
  curvature is a point known as the focal point, F.
• The distance from the mirror to the focal point
  is known as the focal length, f. The focal length
  would be ½ the radius of curvature, R.

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Concave Spherical Mirror
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Real Image

• Imagine a light bulb placed upright behind C, at
  distance p along the principal axis.
• Light rays diverge from the bulb, reflect off the
  mirror and converge at some distance q from the
  mirror.
• The image forms in front of the mirror.
• The image could also be seen on a screen placed
  at the image point.
• An image of this type is called a real image.

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More Real Image

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Mirror Equation

• The equation in terms of radius of curvature is
• 1/p 1/q 2/R
• p object distance
• q image distance
• R radius of curvature
• In terms of focal length the equation is
• 1/p 1/q 1/f
• f focal length

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Sign Conventions

• Object and image distances have a positive sign
  when they are in front of the mirror.
• Distances for images that form to the back side
  of the mirror are always negative.
• Focal length is always positive for a concave
  mirror.
• Object and image heights are positive when above
  the principal axis and negative when below.

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Magnification

• Magnification, M, is defined as the ratio of the
  height of the objects image to its actual
  height.
• Equation for Magnification
• M h/h -q/p
• h image height
• h object height
• q image distance
• p object distance
• M is positive when image is upright and negative
  when its inverted (as compared to the object).

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Ray Diagrams

• For concave mirrors follow the basic procedure
  for a flat mirror, but also measure all distance
  along the principal axis and mark C and F.
• For spherical mirrors, three reference rays are
  used to find the image point.

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More Ray Diagrams (Concave)

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Convex Spherical Mirrors

• A convex spherical mirror is a segment of a
  sphere that is silvered so that light is
  reflected from the spheres outer, convex
  surface.
• This is called a diverging mirror, because the
  incoming rays diverge after reflection as though
  they were coming from some point behind the
  mirror.
• Thus, the resulting image is always virtual. The
  image distance, q, is always negative, as is the
  focal length, f.
• Magnification, M, is always lt 1.

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Ray Diagram (Convex)