Athin spherical glass shell in air is filled with an unknown liquid. a horizontal parallel light beam is incident on the shell and it is observed that the light is brought to focus on the surface of the shell directly opposite of the incoming beam. what is the refractive index of the liquid?
ie. the answer is 2- i just don't know how they got there

I have the exact same question, any chance you figured it out since you posted this?

Neptune is the eighth planet from the sun. it was the first planet to get its existence predicted by  mathematical calculations  before it was actually seen through a telescope on sept. 23, 1846. irregularities in the orbit of  uranus  led french astronomer alexis bouvard to suggest that the gravitational pull from another celestial body might be responsible. german astronomer johann galle then relied on subsequent calculations to   spot neptune via telescope. previously, astronomer galileo galilei sketched the planet, but he mistook it for a star due to its slow motion. in accordance with all the other planets seen in the sky, this new world was given a name from greek and roman mythology — neptune, the roman god of the sea.