Question

A plane convex lens of radius of curvature $6cm$ is placed in air. The thickness of this lens is $3cm$. The focal length of the lens is :

• A. $18cm$
• B. $10cm$
• C. $12cm$
• D. None of these

Answer 1

Answer: (B)

$10cm$

Rays coming from infinite combine at focus

$u=\infty$(at curved refracting surface)

$\begin{array}{cc}\frac{{\mu }_1}{u}-\frac{{\mu }_2}{v}& =\frac{H_1-{\mu }_2}{R}\\ \frac{1}{\infty }-\frac{3}{2v}& =\frac{1-3/2}{6}\\ -\frac{3}{2v}& =-\frac{1}{2\times 6}\\ V& =18cm\end{array}$

Distance & intermediate image from

$\begin{array}{c}\text{plane surface}=18-3=15cm\\ \frac{AD}{RD}=\frac{{\mu }_1}{{\mu }_2}\\ \frac{AD}{15}=\frac{1}{3/2}\\ AD=15\times \frac{2}{3}=10cm\Rightarrow \text{so focal length}=10cm\end{array}$

option $B$ is correct