Concave Mirror Image Example

Question:
A concave mirror has a radius of curvature of 30 cm. An object is located 45 cm from the mirror. Where is the image formed, and what are its properties?

Answer:

• First ray trace: This corresponds almost exactly to the diagram in the upper left hand corner. We expect a real, inverted, image with a magnification less than one. Note that the equation 1/p + 1/q = 1/f works with any length unit.
• Now the algebra:

  Focal length: f = r/2 = 15 cm; object distance: p = 45 cm

  Mirror equation: 1/(45 cm) + 1/q = 1/(15 cm) =>
  1/q = 1/(15 cm) - 1/(45 cm) = 3/(45 cm) - 1/(45 cm) = 2/(45 cm) =>
  q = 22.5 cm

  => The image is formed 22.5 cm in front of the mirror.

• Properties:
  • q > 0 => image is real
  • m = -q/p = -22.5/45 = -0.5
  • m < 0 => the image is inverted
  • |m| = 0.5 < 1 => the image is reduced, exactly half the size of the object.

   

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