Think about what the index means. It's a measure of how refractive a material is, meaning a measure of how much it bends light, right? So if we have a convex lens, we expect it to focus incoming parallel rays to a focal length on the transmitted side. The lens material refracts the light inward. If we increase the refractive index, the lens will bend the light more. Considering which direction the light is being bent, what do you think will happen to the focal point?
You can try it yourself to see, here:
http://phet.colorado.edu/sims/geometric-optics/geometric-optics_en.html