$\textit{a.}$,Since the light is bending away from the normal while travelling in an optically medium with less density and bending towards the normal while travelling in an optically denser medium and we can see that, in medium A, the angle between normal and ray of light is greater than the one in medium B, which shows us that the speed of light is greater in medium A than in medium B, we can finally conclude that medium A is air and medium B is ice.

$\textit{b.}$, Direction is unknown and it does not matter since we have enough information to conclude which medium is which, which does not affect the direction.

a. Medium A is air while medium B is light. Light traveling in an optically denser medium bends towards the normal while it bends away from the normal in an optically less dense medium. It can be seen that in medium A the angle between the normal and the light ray is more than that in medium B, implying that speed of light is greater in medium A than B and hence the conclusion that A is air while B is ice.