An object is placed in front of a concave lens at a distance of 45 cm from it. If its image is formed at a distance of 30 cm from the lens, calculate the focal…

(a) Given,

Object distance (u) = -45 cm

Image distance (v) = -30 cm

From lens formula,

$$\begin{aligned}\frac{1}{\text f} = \frac{1}{\text v} - \frac{1}{\text u} \\[1em] \frac{1}{\text f} = \frac{1}{-30}-\frac{1}{(-45)}\\[1em] \frac{1}{\text f}=-\frac{1}{30}+\frac{1}{45}\\[1em] \frac{1}{\text f} = \frac{-3+2}{90}\\[1em] \frac{1}{\text f} = -\frac{1}{90} \\[1 em] \text f = -\frac{90}{1}\\[1 em] \text f= - 90 \text { cm}\end{aligned}$$