Question

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

Answer 1

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