Question

What is the focal length of double concave lens kept in air with two spherical surfaces of radii $R_1=-20cm$ and $R_2=80cm$. Take refractive index of lens with respect to surrounding as n = 1.5.

Answer 1

Given,
$R_1=-20cm$, $R_2=80cm$, $n=1.5$

Using lens maker's formula,
$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2}$ )
$\frac{1}{f}=(1.5-1)(\frac{1}{-20}-\frac{1}{80}$ )
$\frac{1}{f}=(1.5-1)\left(\frac{-4-1}{80}\right)$
$\frac{1}{f}=(1.5-1)\left(\frac{-5}{80}\right)$
$\frac{1}{f}=\left(0.5\right)\left(\frac{-1}{16}\right)$
$\frac{1}{f}=\frac{-5}{160}$
$\frac{1}{f}=\frac{-1}{32}$
$f=-32cm$