Question

A convex lens has power 10D. When immersed in a liquid it behaves as a concave lens having focal length 50cm. Find refractive index of the liquid.

Answer 1

$$\begin{gathered} DearStudent, \\ accordingtolensmakerformula \\ \frac{1}{f}=\frac{{\mu }_2-{\mu }_1}{{\mu }_1}(\frac{1}{R_1}-\frac{1}{R_2})=\frac{{\mu }_2-{\mu }_1}{{\mu }_1}K \\ inair \\ 10=\frac{1.5-1}{1}K=0.5K-----eq1(assumingforlens=\mu =1.5) \\ inliquid \\ -\frac{1}{0.5}=\frac{1.5-{\mu }_1}{{\mu }_1}K------eq2 \\ dividingeq2byeq1 \\ -2=\frac{1.5-{\mu }_1}{{\mu }_1}\times 20 \\ \Rightarrow {\mu }_1=\frac{5}{3}\left(ans\right) \\ Regards \end{gathered}$$