Question

What is the focal length of a double convex lens kept in air with two spherical surfaces of radii $R_1=30cm$ and $R_2=60cm?$
(Take the refractive index of the lens as $1.5$).

Answer 1

Lens maker formula

$1/F=(u-1)[1|R_1-1|R_2]$

Where $F$ is focal length of lens

$U$ is the refractive index of lens with respect to medium

$R_1$ and $R_2$ are the radius of curvature of both curve surface of lens

given

$n=1.5$

So,$U=n$ relative to vacuum or air

$u=n/1=1.5/1=1.5$

$R_1=-30cm$

$R_2=60cm$

So,

$1/F=(1.5-1)\{\frac{1}{-30}-\frac{1}{60}\}$

$\frac{1}{F}=\left(0.5\right)(\frac{1}{-30}-\frac{-}{60})$

$F=\frac{1}{-0.025}$