Question

A plano convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lens are made of different materials of refractive indices ${\mu }_1$ and ${\mu }_2$ $R$ is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is

• A. $\frac{2R}{M_2-M_1}$
• B. $\frac{R}{2(M_2+M_2)}$
• C. $\frac{R}{2(M_1-M_2)}$
• D. $\frac{R}{{(M_1-M_2)}_1}$

Answer 1

The correct option is D $\frac{R}{{(M_1-M_2)}_1}$

$\begin{array}{cc}\frac{1}{F}& =({\mu }_1,-1)\left(\frac{-1}{R}\right)\\ \frac{1}{F}& -({\mu }_2-1)\left(\frac{1}{R}\right)\\ \frac{1}{r_e}& =\frac{-{\mu }_1}{R}+\frac{1}{R}+\frac{{\mu }_2}{R}-\frac{1}{R}\\ \frac{1}{F_C}& =\frac{{\mu }_2-{\mu }_1}{R}\\ F& =\frac{R}{{\mu }_2-{\mu }_1}\end{array}$

Hence option (D) is correct