Question

A thin biconvex lens having radius of curvature $10\text{cm}$ is placed as shown in figure. Calculate the focal length of the lens, if parallel rays are incident as shown.

• A. $\frac{160}{7}\text{cm}$
• B. $\frac{150}{7}\text{cm}$
• C. $\frac{180}{7}\text{cm}$
• D. $\frac{120}{7}\text{cm}$

Answer 1

The correct option is C $\frac{180}{7}\text{cm}$

As the lens is of converging nature, the parallel rays will converge at focus.

We know,
$\frac{{\mu }_3}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R_1}+\frac{{\mu }_3-{\mu }_2}{R_2}$

Here,
${\mu }_1=\frac{5}{4},{\mu }_2=\frac{5}{3},{\mu }_3=\frac{3}{2}$

$R_1=10\text{cm}$, $R_2=-10\text{cm}$

So, $\frac{3/2}{v}-\frac{5/4}{\infty }=\frac{5/3-5/4}{10}+\frac{3/2-5/3}{(-10)}$

$\Rightarrow v=f=\frac{180}{7}\text{cm}$