Question

You have an hand hold mirror that gives a virtual of your face, enlarged by a factor 1.5,when you hold the mirror 30cm away,what is the mirror s focal length

Answer 1

[tex]\text{We're gonna use the mirror equation, } 1/d_o+1/d_i=1/f.\\ \text{And, the magnification formula, }m=h_i/h_o=-d_i/d_o.\\ \text{We know, } m=1.5\text{ and } d_o=30\text{ cm.}\\ \text{Then, } d_i =(1/f-1/d_o)^{-1}=fd_o/(d_o-f).\\ \text{Thus, } m=-f/(d_o-f)\\ \Rightarrow f=d_om/(m-1)=30\times 1.5/0.5=90\text{ cm.}[/tex]