A convex lens of focal length 10 cm is placed at a distance of 60 cm from a screen. How far from the lens should an object be placed so as to obtain a real image on the screen?
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Given, focal length = 10 cm
Image distance (v) = 60 cm
Object distance (u) = ?
From lens formula —
$$\begin{aligned}\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \\[1em]\end{aligned}$$
Substituting the values in the formula we get,
$$\begin{aligned}\frac{1}{60} - \frac{1}{\text{u}} = \frac{1}{10} \\[1em] \Rightarrow \frac{1}{60} - \frac{1}{10} = \frac{1}{\text{u}} \\[1em] \Rightarrow \frac{1 - 6}{60} = \frac{1}{\text{u}} \\[1em] \Rightarrow \frac{-5}{60} = \frac{1}{\text{u}} \\[1em] \Rightarrow \frac{1}{\text{u}} = \frac{-1}{12} \\[1em] \Rightarrow u = -12\end{aligned}$$
∴ The object should be placed at a distance of 12 cm in front of the lens.