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 $0.5cm$ and refractive index of the material of the lens is $\mathrm{1.5.}$ 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

Answer: 10

$D=4f\Rightarrow f=D/4=0.50$
$\therefore \frac{1}{50}=\left(1.5-1\right)\left(\frac{1}{R}\right)\Rightarrow R=25cm$
$\therefore a=\sqrt{8Rt}\Rightarrow \sqrt{8\times 25\times 0.5}=10cm$