Question

The power of a thin convex lens ${(}_a{\mu }_g=1.5)$ is +5.0 D. When it is placed in a liquid of refractive index ${}_a{\mu }_l$,then it behaves as a concave lens of local length 100 cm. The refractive index of the liquid ${}_a{\mu }_l$ will be

• A. $\frac{5}{3}$
• B. $\frac{4}{3}$
• C. $\sqrt{3}$
• D. $\frac{5}{4}$

Answer 1

The correct option is A $\frac{5}{3}$

By using $\frac{f_l}{f_a}=\frac{{}_a{\mu }_g-1}{{}_l{\mu }_g-1}$; where ${}_l{\mu }_g=\frac{{\mu }_g}{{\mu }_l}=\frac{1.5}{{\mu }_l}$ and $f_a=\frac{1}{p}=\frac{1}{5}m=20cm$
$\Rightarrow \frac{-100}{20}=\frac{1.5-1}{\frac{1.5}{{\mu }_l}-1}\Rightarrow {\mu }_l=\frac{5}{3}$