Question

Find the radii of curvature of a convexo - concave convergent lens made of glass with refractive index $n=1.5$ having focal length of $24cm$. One of the radii of curvature is double the other

Answer 1

Given: a convexo-concave convergent lens made of pf glass with refractive index, $\nu =1.5$ and focal length, $f=24cm$. It has one of the radii of curvature is double the other

To find its radii of the curvature

Solution:

According to the given criteria,

$R_1=2R_2$

for convexo-concave lens $R_1$ is positive and $R_2$ is positive

According to the lens maker formula,

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})⟹\frac{1}{24}=(1.5-1)(\frac{1}{R_1}-\frac{1}{2R_1})⟹\frac{1}{24\times 0.5}=\frac{2-1}{2R_1}⟹R_1=\frac{12}{2}=6cm$

$\therefore ,R_2=2R_1=12cm$

Hence the radii of the curvature is 6cm and 12cm