Question

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

• A. $\frac{R}{{\mu }_1-{\mu }_2}$
• B. $\frac{2R}{{\mu }_2-{\mu }_1}$
• C. $\frac{R}{2({\mu }_1-{\mu }_2)}$
• D. $\frac{R}{2-({\mu }_1+{\mu }_2)}$

Answer 1

The correct option is A $\frac{R}{{\mu }_1-{\mu }_2}$

$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$

or, $\frac{1}{F}=({\mu }_1-1)(\frac{1}{\infty }+\frac{1}{R})+({\mu }_2-1)\left(\frac{1}{-R}\frac{1}{\infty }\right)$
$=\frac{{\mu }_1-{\mu }_2}{R}$
Or, $F=\frac{R}{{\mu }_1-{\mu }_2}$