The focal length of a diverging lens is negative.
f = -12 cm; u = 15 cm.
f=uvu+vf = \frac{uv}{u+v}f=u+vuv
−12=15v15+v-12 = \frac{15v}{15+v}−12=15+v15v
−12(15+v)=15v⇒−180−12v=15v-12(15+v) = 15v \Rightarrow -180 - 12v = 15v−12(15+v)=15v⇒−180−12v=15v
−180=15v+12v⇒−180=27v-180 = 15v + 12v \Rightarrow -180 = 27v−180=15v+12v⇒−180=27v
v=−18027=−6.67 cmv = \frac{-180}{27} = -6.67 \text{ cm}v=27−180=−6.67 cm
The image is virtual and 6.67 cm from the lens.
