Properties of Optical Systems

Example: A converging mirror has a radius of curvature of 25 cm. Objects are placed at (I) 50 cm, (II) 20 cm, and (III) 8 cm from the mirror.

Find the following information:

  • Where is the image formed?
  • Is the image real or virtual?
  • Is the image erect or inverted?
  • Is the image magnified or reduced?


  • R=25\ cm
  • f=\frac{25\ cm}{2}=12.5\ cm
  • d_{0}=50\ cm,\ 20\ cm,\ 8\ cm


  •  d_{i}=???
  • m=???




\frac{1}{12.5}=\frac{1}{d_i}+\frac{1}{50\ cm},\ d_{i}=16.7\ cm → positive means real

M=\frac{-(d_{i})}{d_0}=\frac{-16.7\ cm}{50\ cm}=-0.334=m

  • m<1 → reduced
  • negative → image inverted


\frac{1}{12.5}=\frac{1}{d_i}+\frac{1}{20\ cm},\ d_{i}=33.3\ cmreal

m=\frac{-33.3\ cm}{20\ cm}=-1.67magnified, inverted


\frac{1}{12.5}=\frac{1}{d_i}+\frac{1}{8\ cm},\ d_{i}=-22.2\ cmvirtual

m=\frac{-22.2\ cm}{8\ cm}=2.78erect, magnified