Question

A thin plano - convex lens fits exactly into a thin plano - concave lens. Their plane surfaces 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 surfaces of the lenses, then the focal length of the combination is :

• A. $\frac{R}{{\mu }_2-{\mu }_1}$
• 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 $\frac{R}{{\mu }_2-{\mu }_1}$

The focal length of the combination of lenses will be,

$\frac{1}{f}=({\mu }_1-1)(\frac{1}{\infty }+\frac{1}{R})+({\mu }_2-1)(\frac{1}{\infty }-\frac{1}{R})$
Thus, $f=\frac{R}{{\mu }_2-{\mu }_1}$