The immersion oil has the same refractive index as the glass coverslip and the glass of the objective lens elements (about 1.51). If you have air (refractive index of 1.00) in between the objective and the coverslip, you have extra refraction (the light rays are bent) at the glass-air interface. With a high refractive index oil between the objective and the slide, a good 60X or 100X oil immersion lens will have a numerical aperture of 1.3 - 1.4. Without immersion oil the highest N.A. You can have is about 0.9. If you don't have the immersion oil, you are not able to use the full N.A. Of the objective, which hurts your light collection efficiency (your sample looks dim) and your resolution. Good quality objective lenses from a manufacturer like Nikon or Olympus also have multiple correction elements for various optical aberrations, but if you try to use the objective in a way it wasn't designed for (i.e. By having the wrong refractive index between the objective and the slide) all of these correction elements probably add some extra distortion.
