An object is placed at a distance of 12 cm from a convex lens of focal length 8 cm.

(i) Given,

u = 12 cm (negative),

f = 8 cm (positive)

From lens formula

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Substituting the values we get,

$$\begin{aligned}\frac{1}{v} - \frac{1}{-12} = \frac{1}{8} \\[0.5em] \Rightarrow \frac{1}{v} + \frac{1}{12} = \frac{1}{8} \\[0.5em] \Rightarrow \frac{1}{v} = \frac{1}{8} - \frac{1}{12} \\[0.5em] \Rightarrow \frac{1}{v} = \frac{3 - 2}{24} \\[0.5em] \Rightarrow \frac{1}{v} = \frac{1}{24} \\[0.5em] \Rightarrow v = 24 \text{ cm}\\[0.5em]\end{aligned}$$

The image will be formed at a distance 24 cm behind the lens.

(iii) The image will be real, inverted and magnified.