Question

A plano-convex lens $\left(\mu =\text{1.5}\right)$ has maximum thickness of $1mm$ . If the diameter of its aperture is $4cm$ , then what is the value of its focal length in the air (in $cm$ )?

Answer 1

Answer: 40

$R^2=2^2+(R-0.1{)}^2\Rightarrow R^2=4+R^2+0.01-0.2R$
$0.2R=4.01\Rightarrow R=\frac{4.01}{0.20}$
$=\frac{401}{20}\Rightarrow R=20cm$
from lens formula
$\frac{1}{f}=\left(a{\mu }_g-1\right)\left(\frac{1}{R_1}-\frac{1}{R_2}\right)\Rightarrow \frac{1}{f}=(1.5-1)\left(\frac{1}{20}-\frac{1}{\infty }\right)$
$\frac{1}{f}=\frac{1}{40}\Rightarrow f=40cm$