Question

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

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

Answer 1

The correct option is C

$\frac{R}{({\mu }_1-{\mu }_2)}$

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}=({\mu }_1-1)(\frac{1}{\infty }+\frac{1}{R})+({\mu }_2-1)(-\frac{1}{R}-\frac{1}{\infty })$

$f=\frac{R}{({\mu }_1-{\mu }_2)}$