Question: How does the power of a lens depend on the refractive index of the surrounding medium?

Answer: 
You want the *lens maker's equation* $$\frac{1}{f}=(n\_\mathrm{lens}-n\_\mathrm{medium})\left(\frac{1}{R\_1}-\frac{1}{R\_2}\right)$$ where $R\_1$ and $R\_2$ are the radii of curvature of the two sides of the lens.
It depends on the *difference* between the refractive index of the lens and that of the surrounding medium: the bigger the difference, the stronger the lens. If those are the same, the lens is no longer a lens. If the refractive index of the lens is greater than that of the surrounding medium, then it is a lens and a convex lens like that will bend light to a focal point. On the other hand, if the refractive index of the lens is less that that of the surroundings, then a convex lens like that will disperse a light beam outwards.