Answer: The focal length of the lens = 3.32 cm.
Explanation:
Lens formula : [tex]\dfrac1f=\dfrac1v-\dfrac1u[/tex] (i)
f= focal length , v=image distance , u =object distance.
magnification: m = [tex]\dfrac{v}{u}[/tex] (ii )
Given: v= -12.8 cm , m =2.85
Put values in (ii), we get
[tex]2.85=\dfrac{-12.8}{u}\\\\\Rightarrow\ u=\dfrac{-12.8}{2.85}\\\\\Rightarrow\ u=-4.49\ cm[/tex]
substitute values of u , v in (i)
[tex]\dfrac1f=\dfrac1{-12.8}-\dfrac{1}{4.49}\\\\\Rightarrow\dfrac1f=-0.30084214922\\\\\Rightarrow\ f=\dfrac{-1}{-0.30084214922}\approx3.32\ cm[/tex]
Hence, the focal length of the lens = 3.32 cm.
