Question

A piano-convex lens (refractive index ${\mu }_1$) fits exactly into a piano-concave lens (refractive index ${\mu }_2$). Their plane surfaces are parallel to each other. 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. none of these
  

Answer 1

The correct option is D none of these

$\frac{1}{r}=\frac{{\mu }_1-1}{R}+\frac{1-{\mu }_2}{-R}=\frac{({\mu }_1+{\mu }_2)-2}{R}$

$f=\frac{R}{({\mu }_1+{\mu }_2)-2}$, Hence none of them are correct