Apparent depth when two or more refracting surfaces are present

[esha]

I know the concept of apparent depth as such: It is the depth at which an object is seen when viewed from a different medium. But i want to know what happens when two refracting surfaces are kept one after the other. In the given diagram let the object be placed at the bottom of the vessel. Of course the apparent depth this time wud be different if it would have been only one refracting surface. It is because the emergent ray will converge or diverge (in this case) more. But i don't know how to calculate it.

 

[sophiecentaur]

All that counts is the angle at which the light emerges from the water and enters the eye. We can have absolutely no idea of the path that the light took before that.
In real situations, the eye only sees a narrow range of angles (of course) and the diagrams that people draw are always much exaggerated, which doesn't help.

 

[esha]

but we are able to calculate it when only one surface is present

 

[sophiecentaur]

We can calculate the path for as many surfaces as we want to. But we need to know the layout (multiple lenses calculations etc) first.