Question

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

• A. must be less than 10 cm
• B. must be greater than 200 cm
• C. must not be greater than 200 cm
• D. must not be less than 10 cm

Answer 1

The correct option is D must not be less than 10 cm

If image is to be formed on the screen,

$v-u=40$

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

Using above equations one can write, $\frac{1}{f}=\frac{1}{40+u}-\frac{1}{u}$

Hence $u^2+40u+40f=0$

So there to exist no such u, Determinant of the equation $<0$

Hence, ${40}^2-4\left(1\right)\left(40f\right)<0$

Hence $f>10cm$