Which of the following techniques can be employed to determine the...

To determine the speed of light in a specific medium like water, we need a laboratory method where the required path length of light is relatively small, so that a tube filled with water can be placed in the optical path.

Roemer's method is an astronomical method based on the observation of the eclipses of Jupiter's moons, so it cannot be used to measure the speed of light in water.

Fizeau's method (using a toothed wheel) requires a very long path length (typically several kilometers). It is practically impossible to construct and maintain a water tube of such a large length.

Foucault's method uses a rotating mirror and requires a much shorter path length (a few meters). A tube filled with water can easily be placed between the rotating mirror and the fixed mirror to measure the speed of light in water. Foucault successfully used this to prove that light travels slower in water than in air.

Michelson's method is also a laboratory method (an improvement over Foucault's rotating mirror method) and can be similarly adapted to measure the speed of light in water by placing a water tube in the optical path.

Therefore, both Michelson's method and Foucault's method can be employed.