Deepak and Yumiko are playing a game of hide and seek near a swimming pool that has varying depths from one end to the other. The pool has a gentle slope and is clearly marked with depth indicators along the side. In one part of the game, Deepak, who is it, closes his eyes and counts to one hundred, giving Yumiko time to hide. Yumiko decides to hide in the pool thinking that if she submerges most of her body, she'll be harder to spot. She wades into the pool slowly and stops at a point where the water comes up to her neck. From Deepak's starting point at the pool edge, the depth of the water where Yumiko stands is unknown to him, but he's aware of the slope and the depth indicators.

Yumiko is quite short, and the water level that reaches her neck would only come up to a tall person's waist. As Deepak opens his eyes and begins to search for Yumiko, he approaches the pool but doesn't know exactly where to look because the water distorts the perception of depth. He notices that some parts of the pool are empty and wonders if Yumiko might be standing in a part of the pool where the water is at a certain height on her body.

He recalls from the game's rules that a person is not allowed to fully submerge to hide and that at least the top of the head must be visible. In trying to locate Yumiko, he thinks about the line of sight and the angle of his view relative to the surface of the water. What should Deepak be considering as he looks at the pool water? And what clues can he use to deduce where Yumiko might be hiding based on what he knows about depth perception and refraction at the water's surface?
When Deepak looks at the pool water, he must consider several factors about visibility and perception. First, he should know that due to the refraction of light at the water's surface, objects underwater appear higher than they actually are. Therefore, if he can see part of Yumiko, like the top of her head, he needs to understand it might appear closer to the surface than it actually is. Thus, Deepak can't rely on a straightforward assessment of how deep Yumiko is by what he sees above the water.

He should also be aware that ripples and reflections on the water surface could distort his view, potentially hiding Yumiko's presence in the water even if she's within his line of sight. Moreover, the transparency of the water itself can play a role. If the water is very clear, he may be able to see Yumiko's submerged silhouette from certain angles especially if the light is good and the water serene. If the water is not clear, it would be difficult or impossible to spot her below the surface.

As Yumiko has to keep the top of her head above water, this is the primary visual cue for Deepak. Given his knowledge of the pool's depth indicators, he can approximate areas where someone of Yumiko's height could be submerged up to their neck. The next step is for him to walk alongside the pool, scanning the water surface for any irregularities such as disruptions in the water pattern or protruding objects like hair or head parts which could be due to Yumiko's presence.

Deepak needs to consider his own height and viewing angle. The shallower the water, the easier it will be to see Yumiko from a greater distance. As he moves along, his viewing angle changes, and this might help him see Yumiko's head sticking out of the water where before it might have been camouflaged by surface reflections or the angle was too acute for him to detect her presence. He could also make use of the sun's position: if the sun is behind him, his shadow could alert Yumiko to his presence, making the game less challenging for her.

To further refine his search, he might choose to position himself at points along the pool where the water depth corresponds to what would be waist-high for a taller person. From there, he could look across the pool towards the corresponding depth on the opposite side. If Yumiko is there, he'd be at a good angle to see her head. If not, he can continue this method, moving towards deeper sections and observing the water's surface until he finds a sign of Yumiko.

Yumiko, on the other hand, would be trying to minimize her exposure. If she is strategic, she might choose a spot just deep enough that her head's silhouette against the water surface is minimal, lowering her chances of being spotted while still sticking to the game's rules.

Deepak's success in finding Yumiko will ultimately depend on his understanding of these spatial factors, as well as his observational skills as he systematically examines the pool area, looking for inconsistencies in the water pattern or visible sections of Yumiko's head while considering depth perceptions altered by refraction.