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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:

Known:

Unknowns:

(I)

$\frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_0}$

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

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

(II)

$\frac{1}{12.5}=\frac{1}{d_i}+\frac{1}{20\ cm},\ d_{i}=33.3\ cm$ → real

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

(III)

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

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