If two lenses have the same radii of curvature but different indexes

[needingtoknow]

Homework Statement

If two lenses have the same radii of curvature but different indexes of refraction their focal lengths won't be equal because the one with the greater index of refraction will undergo greater refraction and will have a smaller f. Doesn't this contradict the definition of focal length which states that it has to be half of the radii of curvature?

 

[Vibhor]

Doesn't this contradict the definition of focal length which states that it has to be half of the radii of curvature?

No. This applies in case of a mirror not a lens .

 

[BvU]

My (admittedly rather dusty) memory does't have that kind of 'definition' for focal lenth at all. Who says such a thing ?