$4.(10$ points$)$ A submarine is submerged to a shallow depth in the Pacific ocean on a calm day. An enemy reconnaissance UAV flies over the submarine $3$ km above the surface of water. What is the apparent height of the UAV above the surface as viewed from the submarine? Use both the direct approach involving Snell's law and the small angle approximation and also the approach involving the source$-$image relation for a refractive surface. The index of refraction of the ocean water is $1\mathrm{.}34.$