Glycerine can make a bottle appear invisible due to its refractive index being very close to that of glass. When the refractive indices match, light passes through without bending, causing the bottle to blend seamlessly into the glycerine. This phenomenon occurs because refraction only happens at surfaces where there is a difference in refractive indices. As a result, objects submerged in glycerine can become nearly undetectable. Understanding this principle highlights the relationship between light behavior and material properties.