This is the problem:
A piece of ice floats in a vessel with water above which a layer of a lighter oil is poured. How will the level of the interface (oil and water) change after the whole of ice melts? What will be the change in the total level of liquid in the vessel?
I understood most of the answer to this solution, except this one part. He said the level of interface will change because the volume submerged is greater than the volume of melted ice. This part bugs me, as normally if there was no lighter oil on top, the volume submerged is equal to volume of melted ice (you can figure that out with equations). But here we have oil on top. The teacher justified his answer by saying that the volume submerged will be lower than that of the melted ice because there is a buoyant force acting on ice (by the oil). I don't get why.
How can oil exert buoyant force (there can't be any tangential force on ice because of law of hydrostatics so there can't be any force by oil in the upward direction). In fact I have an argument that says that there will be pressure exerted by oil on the ice from the top making volume of submerged ice to crease. Am I wrong?
Another doubt is intuitively there will be buoyant force on ice that is greater than the usual buoyant force on ice (i.e, in the absence of oil) but I can't find a way to justify with equations. Can someone solve this problem by actual equations and not word explanation so that I can have a better understanding? Can someone solve the specific heights to which interface will rise and liquid falls?