Question

A thin equiconvex lens $(\mu=3 / 2)$ of focal length $10 cm$ is cut and separated and a material of refractive index 3 is filled between them. What is the focal length of the combination?

• A. $-10 \,cm$
• B. $-10 / 4 \,cm$
• C. $-10 / 3\, cm$
• D. None of these

Answer 1

Answer: (C)

$\frac{1}{f}=(\mu-1)\left(\frac{1}{R_{1}}-\frac{1}{R_{2}}\right)$
$R=10\, cm$
$f^{\prime}=(3-1)\left(\frac{1}{-10}-\frac{1}{10}\right)$
$f^{\prime}=\frac{-10}{4}$
$\frac{1}{f_{ eq }}=\frac{1}{20}-\frac{4}{10}+\frac{1}{20}=\frac{2}{20}-\frac{4}{10}$
$f_{ eq }=-10 / 3 \,cm$