Which one has the higher refractive index, cooler air or hotter air?
hotter
cooler
same for both
cannot be determined.
Since hotter air is less dense than cooler air, hence the refractive index of the hotter air is less than the cooler air.
Statement 1 - Apparent position of the object keeps fluctuating when seen through a hot air
Statement2 - Hotter air and cooler air have same refractive index, so no dispersion happens.
Statement 1: on a hot day a straight road from a distance appears wet. This happens because of refraction.
Statement 2: on a hot day the air above the road in contact with the road is hotter and less dense therefore has less refractive index than the cool air above it. When light comes through denser medium to rarer medium(here cooler air to hotter air) it is internally reflected which makes the road appear wet and shiny.