A screen is placed a distance 40 cm away from an illuminated object. A converging lens is placed between the source and the screen and it is attempted to form the image of the source on the screen. If no position could be found, the focal length of the lens

must be greater than 10 cm

Let the distance between source and lens be d.

If image is formed on screen then v = 40 - d

Using lens equation $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ we have

$\frac{1}{40-d}-\frac{1}{-d}=\frac{1}{f} \Rightarrow f=d-\frac{d^2}{40}$

For 'f' to be maximum : $\frac{d f}{d d}=0$

$\Rightarrow 1-\frac{d}{20}=0 \quad \Rightarrow$ d = 20 cm

∴ $f_{\max }=20-\frac{(20)^2}{40}$ = 10 cm

This is maximum value of focal length for which image is formed on screen. But, in question image is not formed.

∴ f > 10 cm