Batman attempts to hide out in a Batbox. The top is a mirrored surface, but the vertical sides are made of clear Batplastic (refractive index np = 1.333). It is located x = 2.74 m horizontally from the edge of the pool.
What is the minimum depth (measured to the top of the Batbox) that the Batbox can be below the surface of the water for the Caped Crusader to remain hidden from the Joker? Assume: The Joker gets down close to the water for the best view.
Answer in units of m.