Question

A dentist uses a spherical mirror to view the tooth of a patient. The required image is to be upright and four times the size of the tooth. Calculate the magnitude of the focal length of the mirror to be used, if the mirror is to be held 1.50 cm from the tooth.

• A. - 1 cm
• B. - 2 cm
• C. - 2.25 cm
• D. - 1.25 cm

Answer 1

The correct option is B - 2 cm

$Objectdis\tan ce,u=-1.5cmMagnification,m=4m=\frac{h_i}{h_o}=\frac{-v}{u}4=\frac{-v}{-1.5}v=6cmSoimagedis\tan ce=5cmNow,bymirrorformula,\frac{1}{f}=\frac{1}{v}+\frac{1}{u}\frac{1}{f}=\frac{1}{6}+\frac{1}{(-1.5)}\frac{1}{f}=\frac{1}{6}+\frac{-4}{6}\frac{1}{f}=\frac{-3}{6}f=-2cmSincethefocallengthcomesouttobenegative,themirrortobeusedisaconcavemirroranditmakesmuchmoresensebecauseonlyaconcavemirrorcanformmagnifiedimages\sin cetheimageisformedbehindthemirrorandisvirtualanderect.$