Question

A plano-convex thin lens is used to obtain the image of a point object $O$ on the screen $S$ as shown in figure. The thickness of the lens in the middle is $0.5\,cm$ and refractive index of the material of the lens is $1.5.$ If the separation $D$ between the object and the screen is to be minimum, then the aperture diameter of the lens (in $cm$ ) should be (consider lens as thin).

Answer 1

$D=4f\Rightarrow f=D/4=0.50$
$\therefore \frac{1}{50}=\left(1 . 5 - 1\right)\left(\frac{1}{R}\right)\Rightarrow R=25\,cm$
$\therefore a=\sqrt{8 R t}\Rightarrow \sqrt{8 \times 25 \times 0 . 5}=10\,cm$