In a long glass tube, mixture of two liquids $A$ and $B$ with refractive indices 1.3 and 1.4 respect

Question

In a long glass tube, mixture of two liquids $A$ and $B$ with refractive indices 1.3 and 1.4 respectively, forms a convex refractive meniscus towards $A$. If an object placed at 13 cm from the vertex of the meniscus in $A$ forms an image with magnification of ' -2 ' then the radius of curvature of meniscus is\

Professor PC Thomas Classes · Answer

(d) : $\frac{n_{2}}{v}-\frac{n_{1}}{u}=\frac{n_{2}-n_{1}}{R}$\ $\frac{1.4}{v}-\frac{1.3}{(-13)}=\frac{0.1}{R}$\ $\frac{1.4}{v}=\frac{1-R}{10 R} \Rightarrow v=\frac{14 R}{(1-R)}$\ As, $m=\frac{v}{n_{2}} 	imes \frac{n_{1}}{u}$\ $=-2=\frac{14 R}{1-R} 	imes \frac{1.3}{1.4} 	imes \frac{1}{(-13)} \Rightarrow 2=\frac{R}{1-R}$,\ $R=\frac{2}{3} \mathrm{~cm}$\