The depth of water in a vessel when seen from air appear to be less because of:
refraction of light
The rays of light diverging from the bottom of the vessel, on emerging out of the water, suffer refraction and hence, bends away from the normal. When these refracted rays reach the eye, then to the eye, they appear to come from the point above the original position. Hence, the depth of the vessel appears to be AI instead of AO. The appearent depth AI is less then real depth AO
Real depthAppearent depth=Refractive index