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Photometry and Geometrical Optics

Problem 5.27

Determine the focal length of a concave mirror if: (a) with the distance between an object and its image being equal to l=15 cm,l=15 \mathrm{~cm}, the transverse magnification β=−2.0\beta=-2.0; (b) in a certain position of the object the transverse magnification is β1=−0.50\beta_{1}=-0.50 and in another position displaced with respect to the former by a distance l=5.0 cml=5.0 \mathrm{~cm} the transverse magnification β2\beta_{2} =−0.25=-0.25

Reveal Answer
(a) f=lβ/(1−β2)=10 cmf=l \beta /\left(1-\beta^{2}\right)=10 \mathrm{~cm} (b) f=lβ1β2/(β2−β1)=2.5cmf=l \beta_{1} \beta_{2} /\left(\beta_{2}-\beta_{1}\right)=2.5cm
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