Would a eyeglass work if the speed of the light was the same in glass as it is in the air?

Answer 1

No. An eyeglass works by bending light (refraction) to change to focal point into something appropriate for whatever eye condition you have (nearsightedness, farsightedness, etc.). The reason that the light bends is that it obeys something known as Fermat's Theorem. Fermat's Theorem says that light takes the fastest travel path (it minimizes travel time, not travel distance) through any medium. Since the speed of light is different in every medium this means that the fastest path doesn't usually follow a straight line if we change mediums. Since light travels more slowly through glass than air, the path bends, hence the refraction, hence the ability of glasses to fix your eyes.

Simply put eyeglasses work precisely because of these two properties:

1) Light has different speeds in different mediums

2) Light always minimizes its total travel time

Answer 2

Yes, eyeglasses would still work even if the speed of light in glass and air were the same. The function of eyeglasses is to bend and focus light so that it reaches the retina properly, regardless of the speed of light in the materials. The refractive index of the materials is what determines how light is bent, not the speed of light.