Q. A thin equiconvex lens is made of glass of refractive index 1.5 and its focal length is $0.2\ m$, if it acts as a concave lens of $0.5\ m$ focal length when dipped in a liquid, the refractive index of the liquid is
A) $\frac{17}{8}$
B) $\frac{15}{8}$
C) $\frac{13}{8}$
D) $\frac{9}{8}$
Explanation
(b) $\frac{f_{l}}{f_{a}} = \frac{\ _{a}\mu_{g} - 1}{\ _{l}\mu_{g} - 1} \Rightarrow \frac{- 0.5}{0.2} = \frac{1.5 - 1}{\ _{l}\mu_{g} - 1} \Rightarrow \ _{l}\mu_{g} - 1 = - 0.2$
$\Rightarrow \ _{l}\mu_{g} = 0.8 = \frac{4}{5} \Rightarrow \frac{\ _{a}\mu_{g}}{\ _{a}\mu_{l}} = \frac{4}{5} \Rightarrow \frac{1.5}{\ _{a}\mu_{l}} = \frac{4}{5}$
$\Rightarrow \ _{a}\mu_{l} = \frac{15}{8}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.