Not very deep!
I have spent a fair number of hours tracking submarines from the air. As already pointed out, you can see a submerged submarine in clear tropical waters, given good lighting conditions. This probably translates to 50–100 feet. However, unless you know exactly where to look, your chances of realizing it is a submarine are remote … unless the periscope is raised. The feather produced by the periscope wake is adequate to draw your attention to the location of the submarine.
Outside of tropical waters, it is extremely difficult to detect a submerged submarine visually. The hull color basically merges with the color of the ocean water. A submarine could be at periscope depth (without periscope exposed), and you will probably not see it. A periscope feather becomes your only visual indication of a submerged submarine and, dependent upon the prevailing conditions, even this may be very challenging.