Is Focal Length Inversely Proportional To Refractive Index?

Is Focal Length Inversely Proportional To Refractive Index? From this formula we can say that focal length of lens is inversely proportional to refractive index of material of lens medium. i.e As Refractive index (m) increases focal length (f) of lens decreases. Is focal length independent of refractive index? A lens works because it has