A convex lens has focal length 12 cm with an object at a distance of 20 cm in front of the lens. He obtains a blurred image on the screen placed at a distance…

away from the lens.

Reason —

Given,

Focal length (f) = +12 cm

Object distance (u) = -20 cm

Blurred image distance (v') = +23 cm

Let, clear image distance be v.

From lens formula,

$$\begin{aligned}\frac{1}{\text f} = \frac{1}{\text v} – \frac{1}{\text u} \\[1 em] \frac{1}{\text v} = \frac{1}{\text f} + \frac{1}{\text u} \\[1 em] \frac{1}{\text v}=\frac{1}{12} + \frac{1}{(-20)}\\[1 em] \frac{1}{\text v}=\frac{1}{12} - \frac{1}{20}\\[1 em] \frac{1}{\text v}=\frac{5-3}{60 }= \frac{2}{60}\\[1 em] \text v = \frac{60}{2} = +30 \text { cm}\end{aligned}$$

Now,

Clear image distance (v) - Blurred image distance (v') = 30 - 23 = 7 cm

So, in order to obtain the clear image, he has to move the screen 7 cm away from the lens.