A convex lens of focal length$10cm$ is placed at a distance of $60cm$from a screen. How far from the lens should be placed an object so as to obtain a real image on the screen? Calculate the magnification of the image and its characteristics.

Step 1: Given data

Distance of the image from the lens$\left(v\right)=60cm$

Distance of object from the lens$\left(u\right)=?$

The focal length of the lens$\left(f\right)=10cm$

---

Step 2: Calculating the distance of the object

Using the lens formula,

$$\begin{gathered} \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \\ \Rightarrow \frac{1}{60}-\frac{1}{u}=\frac{1}{10} \\ \Rightarrow -\frac{1}{u}=\frac{1}{10}-\frac{1}{60} \\ \Rightarrow -\frac{1}{u}=\frac{6-1}{60}=\frac{5}{60}=\frac{1}{12} \end{gathered}$$

Therefore, $u=-12cm$

The negative sign shows that the distance is measured in the opposite direction of the incident light.

---

Step 3: Calculating the magnification

Magnification$=\frac{v}{u}=\frac{60}{-12}=-5$

The magnification is negative and greater than one, so the image will be real, inverted, and enlarged i.e. five times the object.

---

The lens should be placed at$12cm$ to obtain a real image. The magnification is$-5$ and the image will be real, inverted, and enlarged.