Question

Find the focal length of a double convex lens having radius of curvature $R_1=15\text{cm}$ and $R_2=-25\text{cm}$. The refractive index of lens material is $1.5$ and the surrounding medium is air.

• A. $75\text{cm}$
• B. $-75\text{cm}$
• C. $18.75\text{cm}$
• D. $-18.75\text{cm}$

Answer 1

The correct option is C $18.75\text{cm}$

Given that,
$R_1=15\text{cm}$
$R_2=-25\text{cm}$
${\mu }_2=1.5$
${\mu }_1=1$

On applying Lens maker's formula,
$\frac{1}{f}=(\frac{{\mu }_2}{{\mu }_1}-1)(\frac{1}{R_1}-\frac{1}{R_2})$
$\Rightarrow \frac{1}{f}=(\frac{1.5}{1}-1)(\frac{1}{15}-\frac{1}{(-25)})$
$\frac{1}{f}=\left(0.5\right)\left(\frac{5+3}{75}\right)$
$\therefore f=\frac{75}{4}=18.75\text{cm}$