Answer:
Of the king I am blue and of the peasant I am red. Of the frog I am cold and of the dog I am hot instead.
I always have to work with something in my eye.
Taken from a mine and then locked up in a wooden case. I am used by students everyday.
You have to travel far before you turn it over. What is it?
I am lighter than the material I am made of. You see parts of me but more of me is hidden underneath.
Whoever made me don't want me. Whoever bought me don't need me. Whoever use me don't know me.